Hyperscaling relations in mass-deformed conformal gauge theories

TL;DR

This paper derives analytical scaling relations for mass-deformed conformal gauge theories with an IR fixed point, providing tools to distinguish them from confining theories and relating condensate behavior to the Dirac operator spectrum.

Contribution

It presents new RG-based scaling laws for decay constants and condensates in IRFP theories, linking these to the Dirac spectrum and the mass anomalous dimension, aiding interpretation of lattice data.

Findings

Scaling exponents for decay constants derived from RG arguments.

Relation between condensate scaling and Dirac eigenvalue density.

Comparison with numerical data from SU(2) with two adjoint fermions.

Abstract

We present a number of analytical results which should guide the interpretation of lattice data in theories with an infra-red fixed point (IRFP) deformed by a mass term deltaL = - m \bar qq. From renormalization group (RG) arguments we obtain the leading scaling exponent, F ~ m^(eta_F), for all decay constants of the lowest lying states other than the ones affected by the chiral anomaly and the tensor ones. These scaling relations provide a clear cut way to distinguish a theory with an IRFP from a confining theory with heavy fermions. Moreover, we present a derivation relating the scaling of <\bar qq> \sim m^(eta_qq) to the scaling of the density of eigenvalues of the massless Dirac operator rho(lambda) ~ lambda^(eta_qq) RG arguments yield eta_qq = (3-gamma*)/(1+\gamma*)$ as a function of the mass anomalous dimension gamma* at the IRFP. The arguments can be generalized to other condensates such as <G^2> ~ m^(4/(1+gamma*)). We describe a heuristic derivation of the result on the condensates, which provides interesting connections between different approaches. Our results are compared with existing data from numerical studies of SU(2) with two adjoint Dirac fermions.