Then a superfield is a field on superspace which is valued in such a representation.
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.
Superfields were introduced by Abdus Salam and J.
[1] Operations on superfields and a partial classification were presented a few months later by Sergio Ferrara, Julius Wess and Bruno Zumino.
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.
Conventions in this section follow the notes by Figueroa-O'Farrill (2001).
A (anti-)chiral superfield is a supermultiplet of
supersymmetry may be written using the notion of superspace.
Superspace contains the usual space-time coordinates
, transforming as a two-component (Weyl) spinor and its conjugate.
is the covariant derivative, given in index notation as A chiral superfield
The superfield is independent of the 'conjugate spin coordinates'
by convention: this is the F-term which plays an important role in some theories.
The field can then be expressed in terms of the original coordinates
For an action which can be defined from a single chiral superfield, see Wess–Zumino model.
Such a field admits the expansion The constituent fields are Their transformation properties and uses are further discussed in supersymmetric gauge theory.
In this gauge, the expansion takes on the much simpler form Then
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 Fayet (1976); 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
For supermultiplets representing massless particles, on physical grounds the maximum allowed
(which also transform in the adjoint representation of a gauge group).
Such a multiplet can be used to define Seiberg–Witten theory concisely.
vector multiplet contains one gauge field, four Weyl fermions, six scalars, and CPT conjugates.