Суперсимметрия алгебрасының өкілдігі және суперкөліктер

A representation of the supersymmetry algebra
In theoretical physics, a supermultiplet is a representation of a supersymmetry algebra, possibly with extended supersymmetry. Then a superfield is a field on superspace which is valued in such a representation. Naïvely, or when considering flat superspace, a superfield can simply be viewed as a function on superspace. Formally, it is a section of an associated supermultiplet bundle. Phenomenologically, superfields are used to describe particles. It is a feature of supersymmetric field theories that particles form pairs, called superpartners where bosons are paired with fermions. These supersymmetric fields are used to build supersymmetric quantum field theories, where the fields are promoted to operators.

Superfields were introduced by Abdus Salam and J. A. Strathdee in a 1974 article. Operations on superfields and a partial classification were presented a few months later by Sergio Ferrara, Julius Wess and Bruno Zumino.

The most commonly used supermultiplets are vector multiplets, chiral multiplets (in supersymmetry for example), hypermultiplets (in supersymmetry for example), tensor multiplets and gravity multiplets. The highest component of a vector multiplet is a gauge boson, the highest component of a chiral or hypermultiplet is a spinor, the highest component of a gravity multiplet is a graviton. The names are defined so as to be invariant under dimensional reduction, although the organization of the fields as representations of the Lorentz group changes. The use of these names for the different multiplets can vary in literature. A chiral multiplet (whose highest component is a spinor) may sometimes be referred to as a scalar multiplet, and in SUSY, a vector multiplet (whose highest component is a vector) can sometimes be referred to as a chiral multiplet.

For an action which can be defined from a single chiral superfield, see Wess–Zumino model.

A scalar is never the highest component of a superfield; whether it appears in a superfield at all depends on the dimension of the spacetime. For example, in a 10 dimensional N=1 theory the vector multiplet contains only a vector and a Majorana–Weyl spinor, while its dimensional reduction on a d dimensional torus is a vector multiplet containing d real scalars. Similarly, in an 11 dimensional theory there is only one supermultiplet with a finite number of fields, the gravity multiplet, and it contains no scalars. However again its dimensional reduction on a d torus to a maximal gravity multiplet does contain scalars.

A hypermultiplet is a type of representation of an extended supersymmetry algebra, in particular the matter multiplet of supersymmetry in 4 dimensions, containing two complex scalars Ai, a Dirac spinor ψ, and two further auxiliary complex scalars Fi. The name "hypermultiplet" comes from old term "hypersymmetry" for N=2 supersymmetry used by ; this term has been abandoned, but the name "hypermultiplet" for some of its representations is still used.

This section records some commonly used irreducible supermultiplets in extended supersymmetry in the case. These are constructed by a highest weight representation construction in the sense that there is a vacuum vector annihilated by the supercharges The irreps have dimension For supermultiplets representing massless particles, on physical grounds the maximum allowed is , while for renormalizability, the maximum allowed is .

The vector or chiral multiplet contains a gauge field , two Weyl fermions , and a scalar (which also transform in the adjoint representation of a gauge group). These can also be organised into a pair of multiplets, an vector multiplet and chiral multiplet Such a multiplet can be used to define Seiberg–Witten theory concisely. The hypermultiplet or scalar multiplet consists of two Weyl fermions and two complex scalars, or two chiral multiplets.

The vector multiplet contains one gauge field, four Weyl fermions, six scalars, and CPT conjugates. This appears in N = 4 supersymmetric Yang–Mills theory.