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Supermanifold

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.

Supersymmetry

In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry

Supergeometry

Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds. Supergeometry is part and parcel of many classical and quantum field theories i

Graviscalar

In theoretical physics, the hypothetical particle called the graviscalar or radion emerges as an excitation of general relativity's metric tensor, i.e. gravitational field, but is indistinguishable fr

Graviphoton

In theoretical physics and quantum physics, a graviphoton or gravivector is a hypothetical particle which emerges as an excitation of the metric tensor (i.e. gravitational field) in spacetime dimensio

Dilaton

In particle physics, the hypothetical dilaton particle is a particle of a scalar field that appears in theories with extra dimensions when the volume of the compactified dimensions varies. It appears

Superconformal algebra

In theoretical physics, the superconformal algebra is a graded Lie algebra or superalgebra that combines the conformal algebra and supersymmetry. In two dimensions, the superconformal algebra is infin

Harmonic superspace

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

Supermathematics

Supermathematics is the branch of mathematical physics which applies the mathematics of Lie superalgebras to the behaviour of bosons and fermions. The driving force in its formation in the 1960s and 1

Representation of a Lie superalgebra

In the mathematical field of representation theory, a representation of a Lie superalgebra is an action of Lie superalgebra L on a Z2-graded vector space V, such that if A and B are any two pure eleme

Supermetric

Supermetric is a mathematical concept used in a number of fields in physics.

Supersymmetric quantum mechanics

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. Sup

Berezin integral

In mathematical physics, the Berezin integral, named after Felix Berezin, (also known as Grassmann integral, after Hermann Grassmann), is a way to define integration for functions of Grassmann variabl

Supercharge

In theoretical physics, a supercharge is a generator of supersymmetry transformations. It is an example of the general notion of a charge in physics. Supercharge, denoted by the symbol Q, is an operat

No-go theorem

In theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible. Specifically, the term describes results in quantum mechanics like Bell's theor

Superspace

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 coord

Graded manifold

In algebraic geometry, graded manifolds are extensions of the concept of manifolds based on ideas coming from supersymmetry and supercommutative algebra. Both graded manifolds and supermanifolds are p

Superpotential

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 Sch

Adinkra symbols (physics)

In supergravity and supersymmetric representation theory, Adinkra symbols are a graphical representation of supersymmetric algebras. Mathematically they can be described as colored finite connected si

R-symmetry

In theoretical physics, the R-symmetry is the symmetry transforming different supercharges in a theory with supersymmetry into each other. In the simplest case of the N=1 supersymmetry, such an R-symm

Extended supersymmetry

In theoretical physics, extended supersymmetry is supersymmetry whose infinitesimal generators carry not only a spinor index , but also an additional index where is integer (such as 2 or 4). Extended

Supersymmetric theory of stochastic dynamics

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 applicabili

Haag–Łopuszański–Sohnius theorem

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

Conformal supergravity

In theoretical physics, conformal supergravity is the study of the supersymmetrized version of conformal gravity with Weyl transformations. Equivalently, it is the extension of ordinary supergravity t

Super Minkowski space

In mathematics and physics, super Minkowski space or Minkowski superspace is a supersymmetric extension of Minkowski space, sometimes used as the base manifold (or rather, supermanifold) for superfiel

Supermembranes

Supermembranes are hypothesized objects that live in the 11-dimensional theory called M-Theory and should also exist in 11-dimensional supergravity. Supermembranes are a generalisation of superstrings

Supermultiplet

In theoretical physics, a supermultiplet is a representation of a supersymmetry algebra. Then a superfield is a field on superspace which is valued in such a representation. Naïvely, or when consideri

Supersymmetric WKB approximation

In physics, the supersymmetric WKB (SWKB) approximation is an extension of the WKB approximation that uses principles from supersymmetric quantum mechanics to provide estimations on energy eigenvalues

Supersymmetry algebras in 1 + 1 dimensions

A two dimensional Minkowski space, i.e. a flat space with one time and one spatial dimension, has a two-dimensional Poincaré group IO(1,1) as its symmetry group. The respective Lie algebra is called t

Supersymmetry algebra

In theoretical physics, a supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains not only the P

Freund–Rubin compactification

Freund–Rubin compactification is a form of dimensional reduction in which a field theory in d-dimensional spacetime, containing gravity and some field whose field strength is a rank s antisymmetric te

Projective superspace

In supersymmetry, a theory of particle physics, projective superspace is one way of dealing with supersymmetric theories, i.e. with 8 real , in a manifestly covariant manner.

Bogomol'nyi–Prasad–Sommerfield state

In theoretical physics, massive representations of an extended supersymmetry algebra called BPS states have mass equal to the supersymmetry central charge Z. Quantum mechanically, if the supersymmetry

Killing spinor

Killing spinor is a term used in mathematics and physics. By the more narrow definition, commonly used in mathematics, the term Killing spinor indicates those twistorspinors which are also eigenspinor

Dimensional reduction

Dimensional reduction is the limit of a compactified theory where the size of the compact dimension goes to zero. In physics, a theory in D spacetime dimensions can be redefined in a lower number of d

Gauged supergravity

Gauged supergravity is a supergravity theory in which some R-symmetry is gauged such that the gravitinos (superpartners of the graviton) are charged with respect to the gauge fields. Consistency of th

Supergroup (physics)

The concept of supergroup is a generalization of that of group. In other words, every supergroup carries a natural group structure, but there may be more than one way to structure a given group as a s

N = 2 superconformal algebra

In mathematical physics, the 2D N = 2 superconformal algebra is an infinite-dimensional Lie superalgebra, related to supersymmetry, that occurs in string theory and two-dimensional conformal field the

Superstring theory

Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a

Coleman–Mandula theorem

In theoretical physics, the Coleman–Mandula theorem is a no-go theorem stating that spacetime and internal symmetries can only combine in a trivial way. This means that the charges associated with int

Batalin–Vilkovisky formalism

In theoretical physics, the Batalin–Vilkovisky (BV) formalism (named for Igor Batalin and Grigori Vilkovisky) was developed as a method for determining the ghost structure for Lagrangian gauge theorie

Lie superalgebra

In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2‑grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics

Super-Poincaré algebra

In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebr

Supergravity

In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gr

Grassmann number

In mathematical physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber), is an element of the exterior algebra over the complex numbers. The spe

Short supermultiplet

In theoretical physics, a short supermultiplet is a supermultiplet i.e. a representation of the supersymmetry algebra whose dimension is smaller than where is the number of real supercharges. The repr

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