Finite-size scaling tests for spectra in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions

TL;DR

This study investigates the finite-size scaling of the correlation length in SU(3) lattice gauge theory with 12 fundamental fermions, assuming conformality and analyzing data to determine a common scaling exponent.

Contribution

It provides a self-consistent finite-size scaling analysis of correlation lengths in SU(3) gauge theory with 12 flavors, estimating the critical exponent y_m.

Findings

Estimated y_m ~ 1.35 for the correlation length scaling

Identified potential limitations in the finite-size scaling analysis

Supported the conformal hypothesis in the zero-mass, infinite volume limit

Abstract

I carry out a finite-size scaling study of the correlation length in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions, using recent data published by Fodor, Holland, Kuti, Nogradi and Schroeder. I make the assumption that the system is conformal in the zero-mass, infinite volume limit, that scaling is violated by both nonzero fermion mass and by finite volume, and that the scaling function in each channel is determined self-consistently by the data. From several different observables I extract a common exponent for the scaling of the correlation length xi with the fermion mass m_q, xi proportional to m_q to the power -1/y_m, with y_m ~ 1.35. Shortcomings of the analysis are discussed.