RESEARCH STARTER

String Theories

String theories are a collection of theoretical frameworks in physics that conceptualize subatomic particles as tiny, one-dimensional strings rather than zero-dimensional points. This innovative approach emerged during the 1960s and 1970s amid significant advancements in particle physics, particularly with the use of high-energy particle accelerators. The theories aim to unify the four fundamental forces of nature—gravitational, electromagnetic, and the strong and weak nuclear forces—into a comprehensive framework often referred to as a "theory of everything."

Historically, various attempts have been made to combine quantum mechanics with general relativity, but these efforts faced significant mathematical challenges. In the early 1980s, string theory, particularly through the development of superstring theory, began to address these issues by incorporating additional dimensions beyond the commonly recognized four—leading to proposals of ten or even eleven dimensions in total. The discovery of M-theory in 1995 suggested that multiple string theories could be interconnected, highlighting a deeper, unified structure.

Despite its elegance and potential, string theory faces criticism regarding its testability and reliance on complex mathematics. Some progress has been made, such as a successful prediction related to quantum behavior at extreme temperatures, but empirical evidence remains scarce. As string theorists continue to explore and refine these concepts, the theory poses profound questions about the nature of the universe and the fundamental components of matter, potentially influencing our understanding of phenomena like dark matter.

Full Article

  • Type of physical science: Elementary particle (high-energy) physics
  • Field of study: Unified theories

String theory is a set of theories that propose that subatomic particles are hypothetically defined not by points in space and time but by tiny, one-dimensional strings.

Overview

The 1960s and 1970s were remarkable decades in particle physics. Numerous discoveries about subatomic structure were made by physicists gathering data with the aid of enormous high-energy particle accelerators called synchrotrons. Physicists used these machines to accelerate atomic particles to enormously high velocities and crash them into other atomic particles, resulting in a shower of smaller particles as the atomic pieces shattered. Then physicists would study the nature of the new particles, later cataloging and naming them.

German physicist Albert Einstein (1879–1955), with his elegant and revolutionary theories of relativity, demonstrated unequivocally that matter and energy, under the right conditions, are interchangeable. Einstein also firmly believed that every law in physics could be joined into a single, all-encompassing theory he called the unified field theory, also wryly known as “the theory of everything.” Such a theory would unite the four forces of nature: gravitation, electromagnetism, and the strong and weak nuclear forces.

Armed with this knowledge, information from particle-accelerator experiments, and observations of the universe, scientists developed an all-encompassing vision of creation that accounted not only for the formation of the stars and planets but also for all matter itself. This theory, called the Big Bang theory, states that the entire universe began from a tiny pinpoint of energy, infinitely hot and infinitely dense. Nearly 13.8 billion years ago, this tiny point of energy exploded in an unimaginably violent eruption. As the universe expanded, it was at first so hot that it was absolute energy, and no matter could exist at all. As it expanded and cooled, however, tiny particles of matter began to precipitate out of the cloud of energy. These tiny particles came together and ultimately formed what are known as atoms. The first atoms to form were the simplest form of matter, hydrogen, along with some helium.

Although the Big Bang theory describes the origin and evolution of the universe from a scientific point of view, it does not embody a complete, unified field theory. As physicists began to look at the particles that they were creating with their accelerators, their ultimate aim was to construct a unified field theory that would also explain how matter itself formed out of the primordial explosion. They observed that it required more and more energy to divide atomic particles into smaller and smaller pieces. The act of completely disassembling matter seemed to require all the energy of the Big Bang itself, in reverse.

Particle accelerators enable physicists to peer ever deeper into an atom and even into the subparticles of atoms. It is relatively straightforward to calculate how much energy it requires to look into an atom’s innermost parts. Using only the current from a common household outlet, physicists can look into an atom and distinguish the electrons from the atomic nucleus. To look into the nucleus requires far more energy, however, and to probe inside protons and neutrons requires very high energies achievable only in large particle accelerators. Scientists have calculated that to disassemble the atom completely would require a resolution smaller than the Planck length, 1.6 x 10-33 centimeters, and a particle accelerator larger than tens of thousands of solar systems packing the energy of the stars.

In the 1980s, this calculation created something of a crisis in the physics community. Ideally, theoretical physics should be seamlessly joined to experimental physics. Theorists develop theories that are ultimately proved by evidence from particle accelerators. Without supporting evidence, theories cannot develop beyond a hypothesis, and they default to mere conjecture and philosophical musings. One American physicist, Howard Georgi, described this dilemma as having plunged physics into mere “recreational mathematical theology.” Because the energy required to confirm theories seemed to surpass available resources and technology, the physics community embarked on untestable grounds of theory in the early 1980s.

The challenge to develop a single theory of everything has been approached with partial grand unified theories, or GUTs, that join three of the four forces of nature together. Such joining has been largely successful mathematically, but when physicists have attempted to go further or to join such physical concepts as relativity and quantum mechanics, glaring, seemingly absurd errors arise out of massively complex mathematical constructs. These errors are canceled out by a process called renormalization, which means that physicists introduce values into their calculations to cancel out the errors and fit the observations. Hence, some of these theories are incomplete because they cannot exactly predict observed processes without renormalization.

One such attempt was the effort to join quantum mechanics to general relativity, a classical field theory rather than a quantum field theory. Renormalization was not even possible. Finally, a concept was devised called supergravity, in which the graviton, a theorized particle that would hypothetically be responsible for the expression of gravity, had a supersymmetric partner, or superpartner, called a gravitino. Supersymmetry is a theoretical extension of space-time theory in which each boson is associated with a corresponding fermion, and vice versa. Supergravity was a great theoretical construct, but it was seriously deficient in describing the particles that were actually observed in synchrotrons. Until 1984, it was widely believed that supergravity was still the prime contender for the grand unified theory.

In 1919, German physicist Theodor Kaluza, intrigued by Einstein’s view of a four-dimensional universe (width, depth, height, and time), made one of the earliest attempts at a unified field theory by using a fifth dimension to incorporate electromagnetism. Swedish physicist Oskar Klein later linked Kaluza’s idea to quantum mechanics. The Kaluza–Klein theory states that a fifth dimension, of which humans have no manifest awareness, is curled up in a tight circle and plays no part in the observable universe. Positing the existence of this seemingly insignificant and deeply hidden fifth dimension allowed for a partial unification theory. It was such a bizarre concept that it was virtually ignored for more than fifty years.

While the Kaluza–Klein five-dimensional unification concept languished on the shelf, quantum mechanics, which describes the physics of the atomic interior, was born. Quantum physics, like relativity, is often formulated in space-time terms. It describes a subatomic world so divorced from the cause-and-effect, easy-to-understand world of classical physics that even Einstein objected strongly to aspects of its interpretation, although he had made major contributions to quantum theory.

Quantum mechanics clearly won the war with relativity’s classical field theory to describe the subatomic world, and, armed with its often-bizarre philosophical notions, physicists began to peer deeper and deeper into the atomic core. Yet quantum physicists occasionally needed Einstein’s relativistic notions even at atomic distances, and they used them in an untidy merger that constantly necessitated renormalizing and canceling out mathematical absurdities whenever the two disparate sciences were forced to converge.

The initial attempts to look into the atom’s core uncovered discrete particles called protons and neutrons. Using what is known as the standard model, particle physicists found that there are smaller particles still deeper. As they used synchrotrons with higher and higher energies, however, the mathematics of the standard model became less and less effective at explaining the smaller values. Furthermore, the standard model could not account for gravity at quantum distances and masses.

Theoretical physics, despite the strangeness of quantum reality, still had difficulty imagining more than a four-dimensional universe. Modern string theory can be traced back to the 1960s, when Gabriele Veneziano’s work on the strong interaction helped launch the theory, and Yoichiro Nambu later helped develop the idea of one-dimensional strings. These theories used one-dimensional lines that were either open or curled back in on themselves to form a circle—hence the name “string theory.” These one-dimensional strings exist in two topologies, open and closed. An open string has the topology of a line, while a closed string has the topology of a circle. Some modern string theories only incorporate closed strings. String theory defines the distinct particles discovered by the Standard Model as products of the oscillations of a single string.

In 1984, two of string theory’s strongest proponents, John H. Schwarz of the California Institute of Technology and Michael Green of Queen Mary College, London, suggested that merging concepts in string theory with supersymmetry would solve many renormalization problems and mathematical anomalies. This merger also neatly incorporated gravity into quantum physics for the first time. Schwarz and Green called the merged concepts superstring theory.

Before the mid-1990s, there were five distinct superstring theories: type I, type II (encompassing types IIA and IIB), and heterotic (encompassing types SO (32) and E8 × E8, or HO and HE, respectively). All these theories shared some major attributes. They involved a theory of the universe encompassing ten dimensions, nine spatial and one temporal. All three incorporated quantum gravity, free from arbitrary mathematical renormalization. The three theories were considered distinct because of how they dealt with internal symmetry between the grouping characteristics of Standard Model particles and how they approached symmetry between the particles.

In 1995, American theoretical physicist Edward Witten suggested that all five theories—if the two type II theories and the two heterotic theories are considered separate—were, in fact, different aspects of one single unifying theory, which he called M-theory. According to this theory, what were previously thought of as distinct theories were, in fact, related by dualities, which is when two different systems are linked in such a way that they can make equivalent predictions. While the previous string theories posited the existence of ten different dimensions, M-theory assumes the existence of eleven: the four common dimensions and seven higher dimensions. It also includes extended objects called branes, including membranes and five-branes. Theoretically, branes may have as many dimensions as there are spatial dimensions; strings are simply one-dimensional branes, while point particles are zero-dimensional branes, and the membranes from which the term derives are two-dimensional branes.

Understanding the concept of extra dimensions has been a challenge to physicists from the outset of modern physics. The three dimensions of width, depth, and height are obvious realities of the physical world and, as such, require little deliberation to understand just how they fit into any model of physics. Einstein tied time into the physical world through his theories of relativity, and Minkowski’s spacetime formulation treated time as the fourth dimension, mathematically demonstrating the linkage of time and space. When the Kaluza-Klein theory of a universe of more than four dimensions was first contemplated, the ability of physicists or anyone else to look at the universe as it is and clearly understand it through visual observation alone began to break down. Although a fifth dimension could apparently successfully unify electromagnetism with relativity, at least in mathematical theory, the concept of an extra hidden dimension simply could not be visualized in a rational sense outside the enigmatic mathematical paradigms used to describe it. When supersymmetry and superstring theory overtook the Kaluza-Klein theory in the 1980s, it brought with it not one extra dimension but six, and the difficulty in understanding the idea of extra dimensions increased dramatically. In the 1990s, M-theory introduced yet another dimension.

The simplest question that can be asked about these extra dimensions is why they cannot be observed directly. One possible explanation is that although M-theory has ten spatial dimensions, humans experience only three large spatial dimensions; the extra seven dimensions are curled up and embedded in the subatomic world, in a region of space so tiny that they simply cannot be observed directly. Theory predicts that if these extra dimensions do indeed exist, they are confined to regions on the order of the Planck length. To directly observe with particle accelerators anything at such a small scale would require energies that are over one trillion times greater than have ever been produced. Consequently, humans observe the universe on a large scale and see the three-dimensional, smoothed surface of matter that is, in fact, made up of a subsurface with an extraordinarily fine veneer rich in dimensional texture. If string theory is correct, the closest look at the texture of all matter would reveal that the tiniest details of substance are made up not of zero-dimensional points in space but rather of infinitesimal, highly curved, vibrating strings that exist in nine or ten spatial dimensions and are no greater than 10-33 centimeters in length, known as the Planck length.

Applications

The unification theory has come to dominate the thinking of physics. String theory offers the hope of achieving physics’s greatest objective, but it is not without its problems; one of the most common criticisms of string theory is that it is difficult, if not impossible, to test directly. A related development took place in 2009, when experiments involving ultracold gases and quark-gluon plasma showed behavior that could be compared with predictions from string-theory-based methods, but this did not prove string theory correct. However, such opportunities have otherwise been vanishingly rare.

The incorporation of supersymmetry into superstring theory provides opportunities for indirect testing, namely by confirming the existence of predicted superpartners. Confirmation of supersymmetry would not confirm superstring theory in turn, but it would lend the theory some weight. String theorists had hoped that the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN) would provide evidence of these superpartners, but experiments have yet to yield any such evidence.

String theory is a staggeringly complex mathematical construct. Such theories usually begin with simple conceptual notions, and the appropriate mathematics is applied to them later. Einstein’s theories of relativity are examples, and string theory is at just such a stage. To incorporate string theory into the appropriate geometries, however, has required the development of new mathematical methodologies. Juan Maldacena’s 1997 discovery of anti–de Sitter/conformal field theory (AdS/CFT) correspondence, a form of holographic duality that links string theory and quantum field theory, was one such mathematical advance.

Context

String theory may represent the final thrust to develop an experimentally supported grand unified field theory, or it may merely represent a conceptual misstep on the road to the ultimate theory in physics. In either case, string theory has become one of the most intensely developed theories in physics since quantum mechanics opened the doors to the center of the atom in the early twentieth century.

String theory ultimately represents a radical new way of viewing the universe. Just as relativity opened doors to new concepts never before dreamed of by classical physicists, so too has string theory. M-theory proposes a universe of eleven dimensions; how seven extra dimensions in the universe could lie hidden in the depths of all matter is an extraordinary, meaningful philosophical question that may ultimately touch every aspect of science as a whole.

Verification of the existence of hypothetical superpartners would have important implications for cosmology. If their masses and stable lifetimes are as large as string theory predicts, then they could account for a large amount of mass that appears to be missing from the universe, which cosmologists refer to as dark matter. Research on the “swampland” program has explored which string theory models are physically viable and how they may relate to dark energy and cosmic acceleration, though no conclusions have been confirmed.

Developing methods of testing string theory, even indirectly, is a vital task for string theorists. Without the ability to test its theories, even with such elegant representations as string and superstring theory, the very essence of science is rendered ineffective. Throughout history, humanity has sought answers to the fundamental questions about the tiniest parts of all that there is. Some of these answers may lie in the multidimensional, super-small world of superstrings. Researchers have applied string theory mathematics to model complex systems such as biological networks, showing its usefulness beyond fundamental physics. Machine learning techniques have also been used to explore the vast landscape of string theory solutions, helping classify possible models more efficiently.

In the mid-2010s, researchers introduced the “pants” approach—a creative way to study how one string splits into two during interactions. This method made string interactions easier to visualize and analyze mathematically. Physicist Erik Verlinde proposed a new perspective on emergent gravity in 2016, suggesting that gravity is not a fundamental force but arises from the universe’s thermodynamic properties. This perspective offered a new way to explain certain dark matter-related phenomena. In the early 2020s, scientists used pulsar timing array data to improve the precision of cosmic string parameters. In 2024, researchers used string theory to derive new ways of representing π. This discovery reinforced the deep and unexpected links between string theory and pure mathematics.

Principal terms

M-THEORY: a unification of the various superstring theories that introduces an eleventh dimension

PLANCK LENGTH: an exceptionally small subatomic measurement, equal to approximately 1.6 x 10-35 meters

RENORMALIZATION: the process of canceling out absurd mathematical predictions in a physical theory by introducing mathematical factors into equations

RESOLUTION: in subatomic experimentation, the smallest resolvable distance that can be probed with a particle accelerator

STANDARD MODEL: the theoretical model of particle physics developed in the early 1970s

SUPERGRAVITY: a theoretical attempt to unify gravity with elementary particle theory

SUPERSTRING THEORY: a theoretical proposal that defines elementary particles as tiny strings in ten dimensions

SUPERSYMMETRY: a theory that extends the symmetry relationships of the standard model to the Planck scale

SYNCHROTRON: a particle accelerator used in theoretical physics to cause very high-speed collisions between subatomic constituents

TOPOLOGIES: descriptions of the shapes and connectivity of strings or their world sheets, such as open strings or closed strings


Bibliography

Cecotti, Sergio. Introduction to String Theory. Springer, 2023.

Chui, Glennda. “A First: String Theory Predicts an Experimental Result.” Symmetry, Feb. 2009, www.bnl.gov/rhic/string-theory.php. Accessed 30 Apr. 2026.

Cicoli, Michele. “Recent Progress on Inflation and Dark Energy from String Theory.” arXiv, 17 Apr. 2026, arxiv.org/abs/2604.16281. Accessed 30 Apr. 2026.

Crease, Robert P., and Charles C. Mann. The Second Creation. Macmillan, 1986.

Green, Michael B., et al. Superstring Theory. 2 vols., 25th anniv. ed., Cambridge UP, 2012.

Gururaj, Tejasri. “New Tools Are Reshaping How We Explore String Theory.” Interesting Engineering, 11 July 2025, interestingengineering.com/science/string-theory-physics-ai. Accessed 30 Apr. 2026.

Hawking, Stephen W. A Brief History of Time. Bantam, 1988.

Pagels, Heinz R. The Cosmic Code. Bantam, 1982.

Pagels, Heinz R. Perfect Symmetry. Bantam, 1985.

Rebhan, Anton, et al., editors. Strings, Gauge Fields, and the Geometry Behind: The Legacy of Maximilian Kreuzer. World Scientific, 2013.

Schwarz, John H. “Superstrings.” Physics Today, vol. 40, no. 11, 1987, pp. 33–40.

“Scientists Use String Theory to Crack the Code of Natural Networks.” Rensselaer Polytechnic Institute News, 7 Jan. 2026, news.rpi.edu/2026/01/07/scientists-use-string-theory-crack-code-natural-networks. Accessed 30 Apr. 2026.

“Superstrings.” NASA’s Imagine the Universe! NASA, 15 Sept. 2021, imagine.gsfc.nasa.gov/science/questions/cool_superstring_fact.html. Accessed 30 Apr. 2026.

Sutton, Christine. The Particle Connection. Simon, 1984.

West, Peter. Introduction to Strings and Branes. Cambridge UP, 2012.

Wood, Charlie, and Vicky Stein. “What Is String Theory?” Space, 18 May 2023, www.space.com/17594-string-theory.html. Accessed 30 Apr. 2026.

Full Article

  • Type of physical science: Elementary particle (high-energy) physics
  • Field of study: Unified theories

String theory is a set of theories that propose that subatomic particles are hypothetically defined not by points in space and time but by tiny, one-dimensional strings.

Overview

The 1960s and 1970s were remarkable decades in particle physics. Numerous discoveries about subatomic structure were made by physicists gathering data with the aid of enormous high-energy particle accelerators called synchrotrons. Physicists used these machines to accelerate atomic particles to enormously high velocities and crash them into other atomic particles, resulting in a shower of smaller particles as the atomic pieces shattered. Then physicists would study the nature of the new particles, later cataloging and naming them.

German physicist Albert Einstein (1879–1955), with his elegant and revolutionary theories of relativity, demonstrated unequivocally that matter and energy, under the right conditions, are interchangeable. Einstein also firmly believed that every law in physics could be joined into a single, all-encompassing theory he called the unified field theory, also wryly known as “the theory of everything.” Such a theory would unite the four forces of nature: gravitation, electromagnetism, and the strong and weak nuclear forces.

Armed with this knowledge, information from particle-accelerator experiments, and observations of the universe, scientists developed an all-encompassing vision of creation that accounted not only for the formation of the stars and planets but also for all matter itself. This theory, called the Big Bang theory, states that the entire universe began from a tiny pinpoint of energy, infinitely hot and infinitely dense. Nearly 13.8 billion years ago, this tiny point of energy exploded in an unimaginably violent eruption. As the universe expanded, it was at first so hot that it was absolute energy, and no matter could exist at all. As it expanded and cooled, however, tiny particles of matter began to precipitate out of the cloud of energy. These tiny particles came together and ultimately formed what are known as atoms. The first atoms to form were the simplest form of matter, hydrogen, along with some helium.

Although the Big Bang theory describes the origin and evolution of the universe from a scientific point of view, it does not embody a complete, unified field theory. As physicists began to look at the particles that they were creating with their accelerators, their ultimate aim was to construct a unified field theory that would also explain how matter itself formed out of the primordial explosion. They observed that it required more and more energy to divide atomic particles into smaller and smaller pieces. The act of completely disassembling matter seemed to require all the energy of the Big Bang itself, in reverse.

Particle accelerators enable physicists to peer ever deeper into an atom and even into the subparticles of atoms. It is relatively straightforward to calculate how much energy it requires to look into an atom’s innermost parts. Using only the current from a common household outlet, physicists can look into an atom and distinguish the electrons from the atomic nucleus. To look into the nucleus requires far more energy, however, and to probe inside protons and neutrons requires very high energies achievable only in large particle accelerators. Scientists have calculated that to disassemble the atom completely would require a resolution smaller than the Planck length, 1.6 x 10-33 centimeters, and a particle accelerator larger than tens of thousands of solar systems packing the energy of the stars.

In the 1980s, this calculation created something of a crisis in the physics community. Ideally, theoretical physics should be seamlessly joined to experimental physics. Theorists develop theories that are ultimately proved by evidence from particle accelerators. Without supporting evidence, theories cannot develop beyond a hypothesis, and they default to mere conjecture and philosophical musings. One American physicist, Howard Georgi, described this dilemma as having plunged physics into mere “recreational mathematical theology.” Because the energy required to confirm theories seemed to surpass available resources and technology, the physics community embarked on untestable grounds of theory in the early 1980s.

The challenge to develop a single theory of everything has been approached with partial grand unified theories, or GUTs, that join three of the four forces of nature together. Such joining has been largely successful mathematically, but when physicists have attempted to go further or to join such physical concepts as relativity and quantum mechanics, glaring, seemingly absurd errors arise out of massively complex mathematical constructs. These errors are canceled out by a process called renormalization, which means that physicists introduce values into their calculations to cancel out the errors and fit the observations. Hence, some of these theories are incomplete because they cannot exactly predict observed processes without renormalization.

One such attempt was the effort to join quantum mechanics to general relativity, a classical field theory rather than a quantum field theory. Renormalization was not even possible. Finally, a concept was devised called supergravity, in which the graviton, a theorized particle that would hypothetically be responsible for the expression of gravity, had a supersymmetric partner, or superpartner, called a gravitino. Supersymmetry is a theoretical extension of space-time theory in which each boson is associated with a corresponding fermion, and vice versa. Supergravity was a great theoretical construct, but it was seriously deficient in describing the particles that were actually observed in synchrotrons. Until 1984, it was widely believed that supergravity was still the prime contender for the grand unified theory.

In 1919, German physicist Theodor Kaluza, intrigued by Einstein’s view of a four-dimensional universe (width, depth, height, and time), made one of the earliest attempts at a unified field theory by using a fifth dimension to incorporate electromagnetism. Swedish physicist Oskar Klein later linked Kaluza’s idea to quantum mechanics. The Kaluza–Klein theory states that a fifth dimension, of which humans have no manifest awareness, is curled up in a tight circle and plays no part in the observable universe. Positing the existence of this seemingly insignificant and deeply hidden fifth dimension allowed for a partial unification theory. It was such a bizarre concept that it was virtually ignored for more than fifty years.

While the Kaluza–Klein five-dimensional unification concept languished on the shelf, quantum mechanics, which describes the physics of the atomic interior, was born. Quantum physics, like relativity, is often formulated in space-time terms. It describes a subatomic world so divorced from the cause-and-effect, easy-to-understand world of classical physics that even Einstein objected strongly to aspects of its interpretation, although he had made major contributions to quantum theory.

Quantum mechanics clearly won the war with relativity’s classical field theory to describe the subatomic world, and, armed with its often-bizarre philosophical notions, physicists began to peer deeper and deeper into the atomic core. Yet quantum physicists occasionally needed Einstein’s relativistic notions even at atomic distances, and they used them in an untidy merger that constantly necessitated renormalizing and canceling out mathematical absurdities whenever the two disparate sciences were forced to converge.

The initial attempts to look into the atom’s core uncovered discrete particles called protons and neutrons. Using what is known as the standard model, particle physicists found that there are smaller particles still deeper. As they used synchrotrons with higher and higher energies, however, the mathematics of the standard model became less and less effective at explaining the smaller values. Furthermore, the standard model could not account for gravity at quantum distances and masses.

Theoretical physics, despite the strangeness of quantum reality, still had difficulty imagining more than a four-dimensional universe. Modern string theory can be traced back to the 1960s, when Gabriele Veneziano’s work on the strong interaction helped launch the theory, and Yoichiro Nambu later helped develop the idea of one-dimensional strings. These theories used one-dimensional lines that were either open or curled back in on themselves to form a circle—hence the name “string theory.” These one-dimensional strings exist in two topologies, open and closed. An open string has the topology of a line, while a closed string has the topology of a circle. Some modern string theories only incorporate closed strings. String theory defines the distinct particles discovered by the Standard Model as products of the oscillations of a single string.

In 1984, two of string theory’s strongest proponents, John H. Schwarz of the California Institute of Technology and Michael Green of Queen Mary College, London, suggested that merging concepts in string theory with supersymmetry would solve many renormalization problems and mathematical anomalies. This merger also neatly incorporated gravity into quantum physics for the first time. Schwarz and Green called the merged concepts superstring theory.

Before the mid-1990s, there were five distinct superstring theories: type I, type II (encompassing types IIA and IIB), and heterotic (encompassing types SO (32) and E8 × E8, or HO and HE, respectively). All these theories shared some major attributes. They involved a theory of the universe encompassing ten dimensions, nine spatial and one temporal. All three incorporated quantum gravity, free from arbitrary mathematical renormalization. The three theories were considered distinct because of how they dealt with internal symmetry between the grouping characteristics of Standard Model particles and how they approached symmetry between the particles.

In 1995, American theoretical physicist Edward Witten suggested that all five theories—if the two type II theories and the two heterotic theories are considered separate—were, in fact, different aspects of one single unifying theory, which he called M-theory. According to this theory, what were previously thought of as distinct theories were, in fact, related by dualities, which is when two different systems are linked in such a way that they can make equivalent predictions. While the previous string theories posited the existence of ten different dimensions, M-theory assumes the existence of eleven: the four common dimensions and seven higher dimensions. It also includes extended objects called branes, including membranes and five-branes. Theoretically, branes may have as many dimensions as there are spatial dimensions; strings are simply one-dimensional branes, while point particles are zero-dimensional branes, and the membranes from which the term derives are two-dimensional branes.

Understanding the concept of extra dimensions has been a challenge to physicists from the outset of modern physics. The three dimensions of width, depth, and height are obvious realities of the physical world and, as such, require little deliberation to understand just how they fit into any model of physics. Einstein tied time into the physical world through his theories of relativity, and Minkowski’s spacetime formulation treated time as the fourth dimension, mathematically demonstrating the linkage of time and space. When the Kaluza-Klein theory of a universe of more than four dimensions was first contemplated, the ability of physicists or anyone else to look at the universe as it is and clearly understand it through visual observation alone began to break down. Although a fifth dimension could apparently successfully unify electromagnetism with relativity, at least in mathematical theory, the concept of an extra hidden dimension simply could not be visualized in a rational sense outside the enigmatic mathematical paradigms used to describe it. When supersymmetry and superstring theory overtook the Kaluza-Klein theory in the 1980s, it brought with it not one extra dimension but six, and the difficulty in understanding the idea of extra dimensions increased dramatically. In the 1990s, M-theory introduced yet another dimension.

The simplest question that can be asked about these extra dimensions is why they cannot be observed directly. One possible explanation is that although M-theory has ten spatial dimensions, humans experience only three large spatial dimensions; the extra seven dimensions are curled up and embedded in the subatomic world, in a region of space so tiny that they simply cannot be observed directly. Theory predicts that if these extra dimensions do indeed exist, they are confined to regions on the order of the Planck length. To directly observe with particle accelerators anything at such a small scale would require energies that are over one trillion times greater than have ever been produced. Consequently, humans observe the universe on a large scale and see the three-dimensional, smoothed surface of matter that is, in fact, made up of a subsurface with an extraordinarily fine veneer rich in dimensional texture. If string theory is correct, the closest look at the texture of all matter would reveal that the tiniest details of substance are made up not of zero-dimensional points in space but rather of infinitesimal, highly curved, vibrating strings that exist in nine or ten spatial dimensions and are no greater than 10-33 centimeters in length, known as the Planck length.

Applications

The unification theory has come to dominate the thinking of physics. String theory offers the hope of achieving physics’s greatest objective, but it is not without its problems; one of the most common criticisms of string theory is that it is difficult, if not impossible, to test directly. A related development took place in 2009, when experiments involving ultracold gases and quark-gluon plasma showed behavior that could be compared with predictions from string-theory-based methods, but this did not prove string theory correct. However, such opportunities have otherwise been vanishingly rare.

The incorporation of supersymmetry into superstring theory provides opportunities for indirect testing, namely by confirming the existence of predicted superpartners. Confirmation of supersymmetry would not confirm superstring theory in turn, but it would lend the theory some weight. String theorists had hoped that the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN) would provide evidence of these superpartners, but experiments have yet to yield any such evidence.

String theory is a staggeringly complex mathematical construct. Such theories usually begin with simple conceptual notions, and the appropriate mathematics is applied to them later. Einstein’s theories of relativity are examples, and string theory is at just such a stage. To incorporate string theory into the appropriate geometries, however, has required the development of new mathematical methodologies. Juan Maldacena’s 1997 discovery of anti–de Sitter/conformal field theory (AdS/CFT) correspondence, a form of holographic duality that links string theory and quantum field theory, was one such mathematical advance.

Context

String theory may represent the final thrust to develop an experimentally supported grand unified field theory, or it may merely represent a conceptual misstep on the road to the ultimate theory in physics. In either case, string theory has become one of the most intensely developed theories in physics since quantum mechanics opened the doors to the center of the atom in the early twentieth century.

String theory ultimately represents a radical new way of viewing the universe. Just as relativity opened doors to new concepts never before dreamed of by classical physicists, so too has string theory. M-theory proposes a universe of eleven dimensions; how seven extra dimensions in the universe could lie hidden in the depths of all matter is an extraordinary, meaningful philosophical question that may ultimately touch every aspect of science as a whole.

Verification of the existence of hypothetical superpartners would have important implications for cosmology. If their masses and stable lifetimes are as large as string theory predicts, then they could account for a large amount of mass that appears to be missing from the universe, which cosmologists refer to as dark matter. Research on the “swampland” program has explored which string theory models are physically viable and how they may relate to dark energy and cosmic acceleration, though no conclusions have been confirmed.

Developing methods of testing string theory, even indirectly, is a vital task for string theorists. Without the ability to test its theories, even with such elegant representations as string and superstring theory, the very essence of science is rendered ineffective. Throughout history, humanity has sought answers to the fundamental questions about the tiniest parts of all that there is. Some of these answers may lie in the multidimensional, super-small world of superstrings. Researchers have applied string theory mathematics to model complex systems such as biological networks, showing its usefulness beyond fundamental physics. Machine learning techniques have also been used to explore the vast landscape of string theory solutions, helping classify possible models more efficiently.

In the mid-2010s, researchers introduced the “pants” approach—a creative way to study how one string splits into two during interactions. This method made string interactions easier to visualize and analyze mathematically. Physicist Erik Verlinde proposed a new perspective on emergent gravity in 2016, suggesting that gravity is not a fundamental force but arises from the universe’s thermodynamic properties. This perspective offered a new way to explain certain dark matter-related phenomena. In the early 2020s, scientists used pulsar timing array data to improve the precision of cosmic string parameters. In 2024, researchers used string theory to derive new ways of representing π. This discovery reinforced the deep and unexpected links between string theory and pure mathematics.

Principal terms

M-THEORY: a unification of the various superstring theories that introduces an eleventh dimension

PLANCK LENGTH: an exceptionally small subatomic measurement, equal to approximately 1.6 x 10-35 meters

RENORMALIZATION: the process of canceling out absurd mathematical predictions in a physical theory by introducing mathematical factors into equations

RESOLUTION: in subatomic experimentation, the smallest resolvable distance that can be probed with a particle accelerator

STANDARD MODEL: the theoretical model of particle physics developed in the early 1970s

SUPERGRAVITY: a theoretical attempt to unify gravity with elementary particle theory

SUPERSTRING THEORY: a theoretical proposal that defines elementary particles as tiny strings in ten dimensions

SUPERSYMMETRY: a theory that extends the symmetry relationships of the standard model to the Planck scale

SYNCHROTRON: a particle accelerator used in theoretical physics to cause very high-speed collisions between subatomic constituents

TOPOLOGIES: descriptions of the shapes and connectivity of strings or their world sheets, such as open strings or closed strings


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