Conformality Lost

TL;DR

This paper explores mechanisms of conformality loss in quantum theories, identifying three generic scenarios and analyzing their critical behaviors, with implications for phase transitions like the chiral transition in QCD.

Contribution

It classifies three universal mechanisms for conformality loss and connects the critical behavior to known phase transition universality classes, providing new insights into quantum phase transitions.

Findings

Three generic mechanisms for conformality loss identified.

Critical behavior near transition resembles BKT phase transition.

Speculation on the universality class of QCD chiral transition.

Abstract

We consider zero-temperature transitions from conformal to non-conformal phases in quantum theories. We argue that there are three generic mechanisms for the loss of conformality in any number of dimensions: (i) fixed point goes to zero coupling, (ii) fixed point runs off to infinite coupling, or (iii) an IR fixed point annihilates with a UV fixed point and they both disappear into the complex plane. We give both relativistic and non-relativistic examples of the last case in various dimensions and show that the critical behavior of the mass gap behaves similarly to the correlation length in the finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two dimensions, xi ~ exp(c/|T-T_c|^{1/2}). We speculate that the chiral phase transition in QCD at large number of fermion flavors belongs to this universality class, and attempt to identify the UV fixed point that annihilates with the Banks-Zaks fixed point at the lower end of the conformal window.