Conformal Chiral Dynamics

TL;DR

This paper explores the chiral dynamics of gauge theories with infrared fixed points, analyzing fermion condensates, anomalous dimensions, and instanton effects to better understand their phase structure and implications for beyond Standard Model physics.

Contribution

It introduces a generalized Gell-Mann Oakes Renner relation and investigates instanton effects near the fixed point, advancing the understanding of strongly coupled gauge theories.

Findings

Dependence of fermion condensate on fermion mass determined

Instanton contributions significantly affect fixed point dynamics

Generalized Gell-Mann Oakes Renner relation proposed

Abstract

We investigate the chiral dynamics of gauge theories developing an infrared stable fixed point. We determine the dependence of the bilinear fermion condensate on the underlying fermion mass and its anomalous dimension. We introduce the instanton contributions and investigate how they affect the dynamics near the fixed point. We generalize the Gell-Mann Oakes Renner relation and suggest to use it to uncover the presence of an infrared fixed point of the underlying gauge theory. Our results have an immediate impact on the construction of sensible extensions of the Standard Model of particle interactions and the general understanding of the phase diagram of strongly coupled theories.