Geometry of N = 1 super Yang-Mills theory in curved superspace

We give a new description of N = 1 super Yang-Mills (SYM) theory in curved superspace. It is based on the induced geometry approach to a curved superspace in which it is viewed as a surface embedded into C-4/2. The complex structure on C-4/2 supplied with a standard volume element induces a special Cauchy-Riemann (SCR)-structure on the embedded surface. We give an explicit construction of SYM theory in terms of intrinsic geometry of the superspace defined by this SCR-structure and a CR-bundle over the superspace. We write a manifestly SCR-covariant Lagrangian for SYM coupled with matter. We also show that in a special gauge our formulation coincides with the standard one which uses Lorentz connections. Some useful auxiliary results about the integration over surfaces in superspace are obtained.