New Results on the "$a$-theorem" in Four Dimensional Supersymmetric Field Theory

TL;DR

This paper proves that in four-dimensional N=1 supersymmetric theories, the central charge a decreases along RG flows when the U(1)_R current remains conserved, extending the concept of a-maximization beyond fixed points.

Contribution

It introduces an extension of a-maximization applicable to RG flows, providing new insights into the behavior of the a central charge in supersymmetric theories.

Findings

Proves a decreases along RG flows when U(1)_R is conserved.

Extends a-maximization to non-fixed point RG flows.

Provides a new tool for studying supersymmetric RG dynamics.

Abstract

In four dimensional N=1 supersymmetric field theory it is often the case that the $U(1)_R$ current that becomes part of the superconformal algebra at the infrared fixed point is conserved throughout the renormalization group (RG) flow. We show that when that happens, the central charge $a$ decreases under RG flow. The main tool we employ is an extension of recent ideas on ``$a$-maximization'' away from fixed points of the RG. This extension is useful more generally in studying RG flows in supersymmetric theories.