In theoretical physics, there are many theories with supersymmetry (SUSY) which also have internal gauge symmetries. Supersymmetric gauge theory generalizes this notion.

A gauge theory is a field theory with gauge symmetry. Roughly, there are two types of symmetries, global and local. A global symmetry is a symmetry applied uniformly (in some sense) to each point of a manifold. A local symmetry is a symmetry which is position dependent. Gauge symmetry is an example of a local symmetry, with the symmetry described by a Lie group (which mathematically describe continuous symmetries), which in the context of gauge theory is called the gauge group of the theory.

Quantum chromodynamics and quantum electrodynamics are famous examples of gauge theories.

In particle physics, there exist particles with two kinds of particle statistics, bosons and fermions. Bosons carry integer spin values, and are characterized by the ability to have any number of identical bosons occupy a single point in space. They are thus identified with forces. Fermions carry half-integer spin values, and by the Pauli exclusion principle, identical fermions cannot occupy a single position in spacetime. Boson and fermion fields are interpreted as matter. Thus, supersymmetry is considered a strong candidate for the unification of radiation (boson-mediated forces) and matter.

This unification is given by an operator ${\displaystyle Q}$ (or typically many operators), known as a supercharge or supersymmetry generator, which acts schematically as

${\displaystyle Q|{\text{boson}}\rangle =|{\text{fermion}}\rangle }$
${\displaystyle Q|{\text{fermion}}\rangle =|{\text{boson}}\rangle }$

For instance, the supersymmetry generator can take a photon as an argument and transform it into a photino and vice versa. This happens through translation in the (parameter) space. This superspace is a ${\displaystyle {\mathbb {Z} _{2}}}$-graded vector space ${\displaystyle {\mathcal {W}}={\mathcal {W}}^{0}\oplus {\mathcal {W}}^{1}}$, where ${\displaystyle {\mathcal {W}}^{0}}$ is the bosonic Hilbert space and ${\displaystyle {\mathcal {W}}^{1}}$ is the fermionic Hilbert space.

The motivation for a supersymmetric version of gauge theory can be the fact that gauge invariance is consistent with supersymmetry. The first examples were discovered by Bruno Zumino and Sergio Ferrara, and independently by Abdus Salam and James Strathdee in 1974.