Geometry of N=1 Super Yang-Mills Theory in Curved Superspace

TL;DR

This paper presents a novel geometric formulation of N=1 super Yang-Mills theory in curved superspace using an induced geometry approach and SCR-structures, providing explicit constructions and gauge equivalences.

Contribution

It introduces a new geometric description of super Yang-Mills theory in curved superspace based on SCR-structures and embedded surface geometry, linking it to standard formulations.

Findings

Explicit SCR-covariant Lagrangian for SYM with matter

Demonstration of equivalence to standard formulation in a special gauge

Development of auxiliary results for integration over superspace surfaces

Abstract

We give a new description of N=1 super Yang-Mills 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.