Nearly conformal gauge theories in finite volume

TL;DR

This paper investigates nearly conformal SU(3) gauge theories with varying fermion flavors using lattice simulations, identifying phases and analyzing the running of the gauge coupling within finite volumes.

Contribution

It provides new lattice results on the phase structure and dynamics of nearly conformal gauge theories with fermions in the fundamental representation.

Findings

Identification of the chirally broken phase below the conformal window.

Analysis of the spectrum and eigenvalue distributions of the Dirac operator.

First results on the running of the renormalized gauge coupling and beta function.

Abstract

We report new results on nearly conformal gauge theories with fermions in the fundamental representation of the SU(3) color gauge group as the number of fermion flavors is varied in the Nf = 4-16 range. To unambiguously identify the chirally broken phase below the conformal window we apply a comprehensive lattice tool set in finite volumes which includes the test of Goldstone pion dynamics, the spectrum of the fermion Dirac operator, and eigenvalue distributions of random matrix theory. We also discuss the theory inside the conformal window and present our first results on the running of the renormalized gauge coupling and the renormalization group beta function. The importance of understanding finite volume zero momentum gauge field dynamics inside the conformal window is illustrated. Staggered lattice fermions are used throughout the calculations.