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Concept
Supermultiplet
Summary
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.
Conventions in this section follow the notes by .
A general complex superfield in supersymmetry can be expanded as
where are different complex fields. This is not an irreducible supermultiplet, and so different constraints are needed to isolate irreducible representations.
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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 yet undiscovered. If discovered, such superparticles could be candidates for dark matter, and could provide evidence for grand unification or the viability of string theory.
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 (SUSY). Dozens of supersymmetric theories exist. Supersymmetry is a spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi–Dirac statistics.