Chern-Simons Theory on Supermanifolds

TL;DR

This paper develops a geometric framework for quantum field theories on supermanifolds using integral forms and Picture Changing Operators, leading to a consistent action principle for super-Chern-Simons theory.

Contribution

It introduces a novel geometric approach employing integral forms and Picture Changing Operators for supermanifold quantum field theories, specifically constructing a super-Chern-Simons action.

Findings

Established a geometric action principle for N=1 D=3 super-Chern-Simons theory

Utilized integral forms and Picture Changing Operators for supermanifold integration

Provided a foundation for consistent superfield theories on supermanifolds

Abstract

We consider quantum field theories on supermanifolds using integral forms. The latter are used to define a geometric theory of integration and they are essential for a consistent action principle. The construction relies on Picture Changing Operators, analogous to the one introduced in String Theory. As an application, we construct a geometric action principle for N=1 D=3 super-Chern-Simons theory.