Local Couplings and Sl(2,R) Invariance for Gauge Theories at One Loop

TL;DR

This paper investigates the one-loop effective action in gauge theories with local couplings, demonstrating compatibility with SL(2,R) symmetry under Weyl rescaling and discussing potential two-loop effects.

Contribution

It introduces a framework for analyzing local couplings in gauge theories and shows their invariance under SL(2,R) symmetry at one loop, extending understanding of gauge invariance.

Findings

Effective action responds to Weyl rescaling with terms compatible with SL(2,R) symmetry.

Local couplings g(x), θ(x) exhibit invariance under SL(2,R) transformations at one loop.

Discussion of potential modifications at two-loop order.

Abstract

The response of the one loop effective action for a gauge theory with local couplings $g(x),\theta(x)$ under a local Weyl rescaling of the background metric is calculated. Apart from terms which may be removed by local contributions to the effective action the result is compatible with $Sl(2,R)$ symmetry acting on $g,\theta$. Two loop effects are also discussed.