$\sigma$ Model representation of supersymmetric gauge theory

Gauge theory in ordinary superspace is formulated in the language of the bilocal nonlinear model. The basic entity is the principal chiral superfield $b(z,u)$ with values in the algebra of the group of internal symmetry. After the imposition of covariant conditions to eliminate the unimportant goldstonions there is obtained for $b(z,u)$, as in the case of the Minkowski and de Sitter spaces, a “'string” representation in the form of a $P$-exponential of a contour integral of the Yang–Mills superfield $b_A(z)\equiv D_A^ub(z,0)$ along the geodesic in superspace between the points $z+u$ and $z$.