Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories

TL;DR

This paper develops exact formulas to compute the flow of central charges and the Euler anomaly coefficient in N=1 supersymmetric gauge theories, providing evidence for a four-dimensional c-theorem and RG flow irreversibility.

Contribution

It introduces techniques for calculating the evolution of central functions in supersymmetric gauge theories and provides explicit formulas for theories within the conformal window.

Findings

Euler anomaly coefficient always satisfies a_{UV} - a_{IR} > 0

Supports the irreversibility of RG flow in four dimensions

Provides explicit formulas for SU(N_c) gauge theories in the conformal window

Abstract

For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality $% a_{UV}-a_{IR}>0$. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.