Superspace Gauge Fixing of Topological Yang-Mills Theories

TL;DR

This paper develops a superspace formalism for topological Yang-Mills theories, establishing their super-BF structure, and proves their UV finiteness to all orders in perturbation theory.

Contribution

It introduces a superspace approach to construct topological Yang-Mills theories with arbitrary dimensions and supersymmetry, and demonstrates their all-order UV finiteness.

Findings

Unique action determination via super-BF structure

Proof of UV finiteness to all perturbative orders

Generalization to arbitrary dimensions and supersymmetry

Abstract

We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of ``shift supersymmetry'' generators, using a superspace formalism. The super-BF structure of these theories is exploited in orderto determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type.