Constructing a c-function for SUSY Gauge Theories

TL;DR

This paper derives a non-perturbative formula for the RG flow of the Euler density coefficient in N=1 SUSY gauge theories, confirming it with perturbative calculations up to four loops.

Contribution

It introduces a non-perturbative formula for the RG flow of the Euler coefficient in SUSY gauge theories and verifies it against high-order perturbative results.

Findings

Exact agreement with the non-perturbative formula up to 4-loops.

Extension of the approach to general renormalisable theories.

Validation of the formula through perturbative calculations.

Abstract

Recently a non-perturbative formula for the RG flow between UV and IR fixed points of the coefficient in the trace of the energy momentum tensor of the Euler density has been obtained for N=1 SUSY gauge theories by relating the trace and R-current anomalies. This result is compared here with an earlier perturbation theory analysis based on a naturally defined metric on the space of couplings for general renormalisable quantum field theories. This approach is specialised to N=1 supersymmetric theories and extended, using consistency arguments, to obtain the Euler coefficient at fixed points to 4-loops. The result agrees completely, to this order, with the exact formula.