Gauge dependence in topological gauge theories

TL;DR

This paper investigates how gauge choices affect correlators in topological gauge theories, especially when the moduli space boundary introduces gauge dependence, with detailed analysis of 4D topological Yang-Mills on S^4.

Contribution

It parametrizes gauge-fixing freedom in topological gauge theories and analyzes gauge dependence of correlators, highlighting cases with gauge-independent physical meaning.

Findings

Correlators depend on gauge fixing when moduli space has a boundary.

Only a subset of correlators remains gauge independent.

Explicit analysis of 4D topological Yang-Mills on S^4 with instanton number 1.

Abstract

We parametrize the gauge-fixing freedom in choosing the Lagrangian of a topological gauge theory. We compute the gauge-fixing dependence of correlators of equivariant operators when the compactified moduli space has a non-empty boundary and verify that only a subset of these has a gauge independent meaning. We analyze in detail a simple example of such anomalous topological theories, 4D topological Yang-Mills on the four-sphere and instanton number k=1.