Space-time dependent couplings in N=1 SUSY gauge theories: Anomalies and Central Functions

TL;DR

This paper explores space-time dependent couplings in N=1 SUSY gauge theories, deriving the NSVZ beta function via topological anomalies and extending the analysis to curved backgrounds to find an all-order expression for the central charge c.

Contribution

It introduces a novel use of topological anomalies to derive the NSVZ beta function and the central charge c in supersymmetric gauge theories with space-time dependent couplings.

Findings

Derived the NSVZ beta function using topological anomalies.

Extended anomaly analysis to curved superspace backgrounds.

Provided an all-order expression for the central charge c.

Abstract

We consider N=1 supersymmetric gauge theories in which the couplings are allowed to be space-time dependent functions. Both the gauge and the superpotential couplings become chiral superfields. As has recently been shown, a new topological anomaly appears in models with space-time dependent gauge coupling. Here we show how this anomaly may be used to derive the NSVZ beta function in a particular, well-determined renormalisation scheme, both without and with chiral matter. Moreover we extend the topological anomaly analysis to theories coupled to a classical curved superspace background, and use it to derive an all-order expression for the central charge c, the coefficient of the Weyl tensor squared contribution to the conformal anomaly. We also comment on the implications of our results for the central charge a expected to be of relevance for a four-dimensional C-theorem.