The C-Theorem and Chiral Symmetry Breaking in Asymptotically Free Vectorlike Gauge Theories

TL;DR

This paper tests Cardy's c-function in four-dimensional gauge theories with chiral symmetry breaking, showing it consistently decreases from ultraviolet to infrared, supporting its validity in these models.

Contribution

It demonstrates that Cardy's c-function decreases across chiral symmetry breaking in asymptotically free vectorlike gauge theories, assuming the IR limit is set by Goldstone modes.

Findings

The c-function decreases from UV to IR fixed points.

Supports the c-theorem in four-dimensional gauge theories.

Assumes IR limit is determined by Goldstone manifold.

Abstract

We confront Cardy's suggested c-function for four-dimensional field theories with the spontaneous breaking of chiral symmetries in asymptotically free vectorlike gauge theories with fermions transforming according to different representations under the gauge group. Assuming that the infrared limit of the c-function is determined by the dimension of the associated Goldstone manifold, we find that this c-function always decreases between the ultraviolet and infrared fixed points.