Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions

TL;DR

This paper investigates the spectral gap behavior of the massless overlap Dirac operator in three dimensions coupled to abelian fields, revealing phase transitions and measure-dependent spectral properties.

Contribution

It provides new insights into the phase structure and spectral behavior of the Dirac operator with different measures, highlighting measure-dependent gap vanishing mechanisms.

Findings

Identifies strong coupling gapped and weak coupling gapless phases.

Shows Gaussian exponent governs gap vanishing with Maxwell and conformal measures.

Finds non-Gaussian behavior in the compact Thirring measure.

Abstract

The low lying spectrum of the massless overlap Dirac operator coupled to abelian fields in three dimensions with three different measures are shown to exhibit two phases: a strong coupling gapped phase and a weak coupling gapless phase. The vanishing of the gap from the strong coupling side with a Maxwell and a conformal measure is governed by a Gaussian exponent. Contrary to this result, the vanishing of the gap from the strong coupling side with a compact Thirring measure is not consistent with a Gaussian exponent. The low lying spectrum with a non-compact Thirring measure does not exhibit a simple non-monotonic behavior as a function of the lattice size on the weak coupling side. Our combined analysis suggests exploring the possibility of a strongly coupled continuum theory starting from a compact lattice Thirring model where a compact U(1) gauge field with a single link action is coupled to even number of flavors of massless overlap Dirac fermions.