This is a list of quantum field theories. The first few sections are organized according to their matter content, that is, the types of fields appearing in the theory. This is just one of many ways to organize quantum field theories, but reflects the way the subject is taught pedagogically.
Theories whose matter content consists of only scalar fields
Theories whose matter content consists only of spinor fields
Theories whose matter content consists only of gauge fields
Theories studied in the branch of quantum field theory known as string theory. These theories are without supersymmetry.
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In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.
Supersymmetry is a theoretical framework in physics that suggests the existence of a symmetry between particles with integer spin (bosons) and particles with half-integer spin (fermions). It proposes that for every known particle, there exists a partner particle with different spin properties. There have been multiple experiments on supersymmetry that have failed to provide evidence that it exists in nature. If evidence is found, supersymmetry could help explain certain phenomena, such as the nature of dark matter and the hierarchy problem in particle physics.
In theoretical physics, supergravity is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model. Supergravity is the gauge theory of local supersymmetry. Since the supersymmetry (SUSY) generators form together with the Poincaré algebra a superalgebra, called the super-Poincaré algebra, supersymmetry as a gauge theory makes gravity arise in a natural way.
In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories. Type II string theory accounts for two of the five consistent superstring theories in ten dimensions. Both theories have extended supersymmetry which is maximal amount of supersymmetry — namely 32 supercharges — in ten dimensions. Both theories are based on oriented closed strings. On the worldsheet, they differ only in the choice of GSO projection. They were first discovered by Michael Green and John Henry Schwarz in 1982, with the terminology of type I and type II coined to classify the three string theories known at the time.
In quantum field theory, the term moduli is sometimes used to refer to scalar fields whose potential energy function has continuous families of global minima. Such potential functions frequently occur in supersymmetric systems. The term "modulus" is borrowed from mathematics, where it is used synonymously with "parameter". The word moduli first appeared in 1857 in Bernhard Riemann's celebrated paper "Theorie der Abel'schen Functionen".
In theoretical physics, there are many theories with supersymmetry (SUSY) which also have internal gauge symmetries. Supersymmetric gauge theory generalizes this notion.
In theoretical physics, the Wess–Zumino model has become the first known example of an interacting four-dimensional quantum field theory with linearly realised supersymmetry. In 1974, Julius Wess and Bruno Zumino studied, using modern terminology, dynamics of a single chiral superfield whose cubic superpotential leads to a renormalizable theory. It is a special case of 4D N = 1 global supersymmetry.
Julius Erich Wess was an Austrian theoretical physicist noted as the co-inventor of the Wess–Zumino model and Wess–Zumino–Witten model in the field of supersymmetry and conformal field theory. He was also a recipient of the Max Planck medal, the Wigner medal, the Gottfried Wilhelm Leibniz Prize, the Heineman Prize, and of several honorary doctorates.
In theoretical physics, the Haag–Łopuszański–Sohnius theorem states that if both commutating and anticommutating generators are considered, then the only way to nontrivially mix spacetime and internal symmetries is through supersymmetry. The anticommutating generators must be spin-1/2 spinors which can additionally admit their own internal symmetry known as R-symmetry. The theorem is a generalization of the Coleman–Mandula theorem to Lie superalgebras. It was proved in 1975 by Rudolf Haag, Jan Łopuszański, and Martin Sohnius as a response to the development of the first supersymmetric field theories by Julius Wess and Bruno Zumino in 1974.
Bruno Zumino was an Italian theoretical physicist and faculty member at the University of California, Berkeley. He obtained his DSc degree from the University of Rome in 1945.
Sergio Ferrara is an Italian physicist working on theoretical physics of elementary particles and mathematical physics. He is renowned for the discovery of theories introducing supersymmetry as a symmetry of elementary particles and of supergravity, the first significant extension of Einstein's general relativity, based on the principle of "local supersymmetry". He is an emeritus staff member at CERN and a professor emeritus at the University of California, Los Angeles.
William Allan Bardeen is an American theoretical physicist who worked at the Fermi National Accelerator Laboratory. He is renowned for his foundational work on the chiral anomaly, the Yang-Mills and gravitational anomalies, the development of quantum chromodynamics and the scheme frequently used in perturbative analysis of experimentally observable processes such as deep inelastic scattering, high energy collisions and flavor changing processes.
In theoretical physics a nonrenormalization theorem is a limitation on how a certain quantity in the classical description of a quantum field theory may be modified by renormalization in the full quantum theory. Renormalization theorems are common in theories with a sufficient amount of supersymmetry, usually at least 4 supercharges.
This page is a glossary of terms in string theory, including related areas such as supergravity, supersymmetry, and high energy physics.
N = 4 supersymmetric Yang–Mills (SYM) theory is a relativistic conformally invariant Lagrangian gauge theory describing fermions interacting via gauge field exchanges. In D=4 spacetime dimensions, N=4 is the maximal number of supersymmetries or supersymmetry charges.
In four spacetime dimensions, N = 8 supergravity, speculated by Stephen Hawking, is the most symmetric quantum field theory which involves gravity and a finite number of fields. It can be found from a dimensional reduction of eleven-dimensional supergravity by making the size of seven of the dimensions go to zero. It has eight supersymmetries, which is the most any gravitational theory can have, since there are eight half-steps between spin 2 and spin −2. More supersymmetries would mean the particles would have superpartners with spins higher than 2. The only theories with spins higher than 2 which are consistent involve an infinite number of particles. Stephen Hawking in his Brief History of Time speculated that this theory could be the Theory of Everything. However, in later years this was abandoned in favour of string theory. There has been renewed interest in the 21st century, with the possibility that this theory may be finite.
Ali H. Chamseddine is a Lebanese physicist known for his contributions to particle physics, general relativity and mathematical physics. As of 2013, Chamseddine is a physics Professor at the American University of Beirut and the Institut des hautes études scientifiques.
Peter Christopher West, born on 4 December 1951, is a British theoretical physicist at King's College, London and a fellow of the Royal Society.
In theoretical physics, more specifically in quantum field theory and supersymmetry, supersymmetric Yang–Mills, also known as super Yang–Mills and abbreviated to SYM, is a supersymmetric generalization of Yang–Mills theory, which is a gauge theory that plays an important part in the mathematical formulation of forces in particle physics. It is a special case of 4D N = 1 global supersymmetry.
In supersymmetry, 4D global supersymmetry is the theory of global supersymmetry in four dimensions with a single supercharge. It consists of an arbitrary number of chiral and vector supermultiplets whose possible interactions are strongly constrained by supersymmetry, with the theory primarily fixed by three functions: the Kähler potential, the superpotential, and the gauge kinetic matrix. Many common models of supersymmetry are special cases of this general theory, such as the Wess–Zumino model, super Yang–Mills theory, and the Minimal Supersymmetric Standard Model. When gravity is included, the result is described by 4D supergravity.