Conformal anomaly from gauge fields without gauge fixing

TL;DR

This paper demonstrates a gauge-invariant method to compute the Weyl anomaly for gauge fields using exact renormalization group equations without gauge fixing, employing covariant regularization and supergauge embedding.

Contribution

It introduces a gauge-invariant approach to calculate the Weyl anomaly via exact renormalization group equations without gauge fixing, utilizing covariant higher derivatives and supergauge embedding.

Findings

Successfully computes Weyl anomaly without gauge fixing.

Develops a supergauge invariant flow equation for Maxwell fields.

Provides a novel regularization scheme preserving gauge invariance.

Abstract

We show how the Weyl anomaly generated by gauge fields, can be computed from manifestly gauge invariant and diffeomorphism invariant exact renormalization group equations, without having to fix the gauge at any stage. Regularisation is provided by covariant higher derivatives and by embedding the Maxwell field into a spontaneously broken $U(1|1)$ supergauge theory. We first provide a realisation that leaves behind two versions of the original $U(1)$ gauge field, and then construct a manifestly $U(1|1)$ supergauge invariant flow equation which leaves behind only the original Maxwell field in the spontaneously broken regime.