Superspace is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions x, y, z, ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numbers rather than real numbers. The ordinary space dimensions correspond to bosonic degrees of freedom, the anticommuting dimensions to fermionic degrees of freedom.
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.
The Minimal Supersymmetric Standard Model (MSSM) is an extension to the Standard Model that realizes supersymmetry. MSSM is the minimal supersymmetrical model as it considers only "the [minimum] number of new particle states and new interactions consistent with "Reality". Supersymmetry pairs bosons with fermions, so every Standard Model particle has a superpartner. If discovered, such superparticles could be candidates for dark matter, and could provide evidence for grand unification or the viability of string theory. The failure to find evidence for MSSM using the Large Hadron Collider has strengthened an inclination to abandon it.
In theoretical physics, a supermultiplet is a representation of a supersymmetry algebra, possibly with extended supersymmetry.
In physics and mathematics, supermanifolds are generalizations of the manifold concept based on ideas coming from supersymmetry. Several definitions are in use, some of which are described below.
In theoretical physics, the superpotential is a function in supersymmetric quantum mechanics. Given a superpotential, two "partner potentials" are derived that can each serve as a potential in the Schrödinger equation. The partner potentials have the same spectrum, apart from a possible eigenvalue of zero, meaning that the physical systems represented by the two potentials have the same characteristic energies, apart from a possible zero-energy ground state.
In theoretical physics, supersymmetric quantum mechanics is an area of research where supersymmetry are applied to the simpler setting of plain quantum mechanics, rather than quantum field theory. Supersymmetric quantum mechanics has found applications outside of high-energy physics, such as providing new methods to solve quantum mechanical problems, providing useful extensions to the WKB approximation, and statistical mechanics.
In theoretical physics, one often analyzes theories with supersymmetry in which F-terms play an important role. In four dimensions, the minimal N=1 supersymmetry may be written using a superspace. This superspace involves four extra fermionic coordinates , transforming as a two-component spinor and its conjugate.
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.
In theoretical physics, topological string theory is a version of string theory. Topological string theory appeared in papers by theoretical physicists, such as Edward Witten and Cumrun Vafa, by analogy with Witten's earlier idea of topological quantum field theory.
In theoretical physics, Seiberg–Witten theory is an supersymmetric gauge theory with an exact low-energy effective action, of which the kinetic part coincides with the Kähler potential of the moduli space of vacua. Before taking the low-energy effective action, the theory is known as supersymmetric Yang–Mills theory, as the field content is a single vector supermultiplet, analogous to the field content of Yang–Mills theory being a single vector gauge field or connection.
In supersymmetry, harmonic superspace is one way of dealing with supersymmetric theories with 8 real SUSY generators in a manifestly covariant manner. It turns out that the 8 real SUSY generators are pseudoreal, and after complexification, correspond to the tensor product of a four-dimensional Dirac spinor with the fundamental representation of SU(2)R. The quotient space , which is a 2-sphere/Riemann sphere.
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.
In theoretical physics, the Fayet–Iliopoulos D-term is a D-term in a supersymmetric theory obtained from a vector superfield V simply by an integral over all of superspace:
This page is a glossary of terms in string theory, including related areas such as supergravity, supersymmetry, and high energy physics.
In mathematics and physics, super Minkowski space or Minkowski superspace is a supersymmetric extension of Minkowski space, sometimes used as the base manifold for superfields. It is acted on by the super Poincaré algebra.
N = 4 supersymmetric Yang–Mills (SYM) theory is a relativistic conformally invariant Lagrangian gauge theory describing the interactions of fermions via gauge field exchanges. In D=4 spacetime dimensions, N=4 is the maximal number of supersymmetries or supersymmetry charges.
Supersymmetric theory of stochastic dynamics or stochastics (STS) is an exact theory of stochastic (partial) differential equations (SDEs), the class of mathematical models with the widest applicability covering, in particular, all continuous time dynamical systems, with and without noise. The main utility of the theory from the physical point of view is a rigorous theoretical explanation of the ubiquitous spontaneous long-range dynamical behavior that manifests itself across disciplines via such phenomena as 1/f, flicker, and crackling noises and the power-law statistics, or Zipf's law, of instantonic processes like earthquakes and neuroavalanches. From the mathematical point of view, STS is interesting because it bridges the two major parts of mathematical physics – the dynamical systems theory and topological field theories. Besides these and related disciplines such as algebraic topology and supersymmetric field theories, STS is also connected with the traditional theory of stochastic differential equations and the theory of pseudo-Hermitian operators.
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.
