Nonlocal regularisation and two-dimensional induced actions

TL;DR

This paper introduces a novel invariant regularisation method for two-dimensional induced gauge theories, clarifying their locality properties and providing a simple proof regarding the $\

Contribution

It presents a new regularisation scheme that is local in Polyakov's variables and nonlocal in gauge potentials, advancing understanding of induced actions and anomalies.

Findings

The regularisation scheme clarifies the locality of induced actions.

The proof shows the $\

The $\

Abstract

We present an invariant regularisation scheme to compute two dimensional induced gauge theory actions, that is local in Polyakov's variables, but nonlocal in the original gauge potentials. Our method sheds light on the locality of this induced action, and leads to a straightforward proof that the $\varepsilon$-anomaly in $W_3$-gravity is completely given by the one loop term.