Vector supersymmetry in topological field theories

TL;DR

This paper provides a straightforward derivation of vector supersymmetry transformations in topological field theories, reproducing known results and discovering new transformations in four-dimensional topological Yang-Mills theories.

Contribution

It introduces a simple method to derive vector supersymmetry transformations, including new transformations for 4d topological Yang-Mills theories, enhancing understanding of their symmetry structures.

Findings

Reproduces known vector supersymmetry transformations

Derives new transformations for 4d topological YM theories

Provides a concise derivation method similar to BRST transformations

Abstract

We present a simple derivation of vector supersymmetry transformations for topological field theories of Schwarz- and Witten-type. Our method is similar to the derivation of BRST-transformations from the so-called horizontality conditions or Russian formulae. We show that this procedure reproduces in a concise way the known vector supersymmetry transformations of various topological models and we use it to obtain some new transformations of this type for 4d topological YM-theories in different gauges.