GMOR-like relation in IR-conformal gauge theories

TL;DR

This paper extends the GMOR relation to infrared-conformal gauge theories, analyzing how the pseudoscalar susceptibility and chiral condensate relate in these theories, with implications depending on the anomalous dimension.

Contribution

It provides a generalized GMOR relation for IR-conformal theories and analyzes the spectral contributions and behavior based on the anomalous dimension.

Findings

Pseudoscalar susceptibility is not saturated by the lightest state in IR-conformal theories.

The behavior of the theory depends on whether the anomalous dimension is less than or greater than 1.

Continuum spectrum contributions persist in the chiral limit.

Abstract

A generalization of the GMOR relation to the case of infrared-conformal gauge theories is discussed. The starting point is the chiral Ward identity connecting the isovector pseudoscalar susceptibility to the chiral condensate, in a mass-deformed theory. A renormalization-group analysis shows that the pseudoscalar susceptibility is not saturated by the lightest state, but a contribution from the continuum part of the spectrum survives in the chiral limit. The computation also shows how infrared-conformal gauge theories behave differently, depending on whether the anomalous dimension of the chiral condensate be smaller or larger than 1.