A precise determination of the psibar-psi anomalous dimension in conformal gauge theories

TL;DR

This paper presents a lattice simulation method to accurately determine the psibar-psi anomalous dimension in conformal gauge theories using spectral density scaling, demonstrated on SU(2) with 2 adjoint fermions.

Contribution

It introduces a cost-effective, robust strategy based on spectral density scaling to compute the anomalous dimension at fixed points in conformal gauge theories.

Findings

Anomalous dimension in SU(2) with 2 adjoint fermions is 0.371(20).

Method is highly accurate and requires no scaling in Lagrangian parameters.

Strategy is effective and robust for conformal gauge theories.

Abstract

A strategy for computing the psibar-psi anomalous dimension at the fixed point in infrared-conformal gauge theories from lattice simulations is discussed. The method is based on the scaling of the spectral density of the Dirac operator or rather its integral, the mode number. It is relatively cheap, mainly for two reasons: (a) the mode number can be determined with quite high accuracy, (b) the psibar-psi anomalous dimension is extracted from a fit of several observables on the same set of configurations (no scaling in the Lagrangian parameters is needed). As an example the psibar-psi anomalous dimension has been computed in the SU(2) theory with 2 Dirac fermions in the adjoint representation of the gauge group, and has been found to be 0.371(20). In this particular case, the proposed strategy has proved to be very robust and effective.