Topological Yang-Mills theories in self-dual and anti-self-dual Landau gauges revisited

TL;DR

This paper revisits the renormalizability of topological Yang-Mills theories in self-dual and anti-self-dual Landau gauges, demonstrating that all two-point functions are exactly determined at tree level due to Ward identities.

Contribution

It proves the renormalizability of these theories with only one independent renormalization and derives exact features of two-point functions using algebraic methods.

Findings

All two-point functions are tree-level exact.

Only one independent renormalization is needed.

Ward identities constrain the two-point functions.

Abstract

We reconsider the renormalizability of topological Yang-Mills field theories in (anti-)self-dual Landau gauges. By employing algebraic renormalization techniques we show that there is only one independent renormalization. Moreover, due to the rich set of Ward identities, we are able to obtain some important exact features of the (connected and one-particle irreducible) two-point functions. Specifically, we show that all two-point functions are tree-level exact.