Large-N reduction in QCD-like theories with massive adjoint fermions

TL;DR

This paper demonstrates that large-N QCD with massive adjoint fermions exhibits volume independence, allowing the study of large-volume physics through reduced models and Monte Carlo simulations, confirming confinement/deconfinement transitions.

Contribution

It provides analytical and numerical evidence for large-small volume equivalence in massive adjoint fermion QCD and introduces twisted models to improve finite-N corrections.

Findings

Existence of center-symmetric phase at small volume for any finite mass.

Confirmation of volume independence via Monte Carlo simulations.

Observation of confinement/deconfinement transition consistent with large-volume Yang-Mills results.

Abstract

Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R^3 x S^1 can be studied via a unitary matrix quantum mechanics on S^1, by varying the temperature. To confirm this non-perturbatively, we numerically study both zero- and one-dimensional theories by using Monte-Carlo simulation. Order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1^3 x 2-lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a non-perturbative formulation of the non-commutative Yang-Mills theory.