Large Nc volume reduction and chiral random matrix theory

TL;DR

This paper investigates chiral symmetry breaking in large-Nc SU(Nc) gauge theories with adjoint fermions using volume reduction and chiral random matrix theory, confirming symmetry breaking in the quenched approximation.

Contribution

It demonstrates the application of large-Nc volume reduction combined with chRMT to detect chiral symmetry breaking, even when the chRMT and 't Hooft limits are not fully compatible.

Findings

Heavy adjoint fermions preserve center symmetry and enable volume reduction.

Chiral symmetry breaking is confirmed via Dirac spectrum analysis.

Methodology established for future studies beyond quenched approximation.

Abstract

Motivated by recent progress on the understanding of the Eguchi-Kawai (EK) volume equivalence and growing interest in conformal window, we simultaneously use the large-Nc volume reduction and Chiral Random Matrix Theory (chRMT) to study the chiral symmetry breaking of four dimensional SU(Nc) gauge theory with adjoint fermions in the large Nc limit. Although some cares are required because the chRMT limit and 't Hooft limit are not compatible in general, we show that the breakdown of the chiral symmetry can be detected in large-Nc gauge theories. As a first step, we mainly focus on the quenched approximation to establish the methodology. We first confirm that heavy adjoint fermions, introduced as the center symmetry preserver, work as expected and thanks to them the volume reduction holds. Using massless overlap fermion as a probe, we then calculate the low-lying Dirac spectrum for fermion in the adjoint representation to compare to that of chRMT, and find that chiral symmetry is indeed broken in the quenched theory.