supermultiplet

A supermultiplet is a representation of the supersymmetry algebra that packages together states related by supersymmetry transformations. Each supermultiplet contains both bosonic and fermionic states, and the numbers of on-shell bosonic and fermionic degrees of freedom match within the representation.

In four-dimensional theories with N=1 supersymmetry, the two basic irreducible multiplets are the chiral multiplet and the vector multiplet. A chiral multiplet contains a complex scalar field and a Weyl fermion; a vector multiplet contains a gauge field and a gaugino, together with auxiliary fields that ensure the algebra closes off-shell. These multiplets form the building blocks of many supersymmetric models, such as the Wess–Zumino model and supersymmetric gauge theories.

In theories with extended supersymmetry (N>1), multiplets are larger and come in families such as hypermultiplets and vector multiplets. For example, in N=2, the vector multiplet includes a gauge field, a complex scalar, and two Weyl fermions, while the hypermultiplet contains two complex scalars and two Weyl fermions. In N=4 super Yang–Mills theory, a single vectormultiplet contains a gauge field, four fermions, and six real scalars. Extended supersymmetry also allows shortening conditions, leading to shorter (BPS) multiplets with fewer states.

Supermultiplets are representations of the super-Poincaré algebra and can be realized with superfields in superspace. Off-shell closure typically requires auxiliary fields, whereas on-shell the multiplets exhibit equal bosonic and fermionic degrees of freedom and are connected by supersymmetry transformations.