What is "supermultiplet"

n. (context physics English) A set of quantum mechanical states, each of which has the same value for a certain quantum number (or numbers) but different values for another related one

In theoretical physics, a supermultiplet is a representation of a supersymmetry algebra. It consists of a collection of particles, called superpartners, corresponding to operators in a quantum field theory which in superspace are represented by superfields.

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

The most commonly used supermultiplets are vector multiplets, chiral multiplets (in 4d N=1 supersymmetry for example), hypermultiplets (in 4d N=2 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.

Note, however, that the use of these names for the different multiplets can vary in literature. Sometimes a chiral multiplet (whose highest component is a spinor) can be referred to as a scalar multiplet. Also, in N=2 SUSY, a vector multiplet (whose highest component is a vector) can sometimes be referred to as a chiral multiplet.

Especially in theories with extended supersymmetry, supermultiplets can be divided to short supermultiplets and long supermultiplets, essentially according to the dimensionality. The short supermultiplets coincide with the BPS states.

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.