Finite size phase transitions in QCD with adjoint fermions

TL;DR

This study explores the phase structure of lattice QCD with adjoint fermions on a compactified space, revealing multiple phases with different center symmetry realizations and their impact on chiral symmetry, relevant to volume independence conjectures.

Contribution

It provides the first detailed lattice analysis of phase transitions and center symmetry realizations in adjoint QCD with varying compactification sizes.

Findings

Four distinct phases with different center symmetry states.

Chiral symmetry remains broken at phase transitions.

Potential implications for volume independence in large Nc limit.

Abstract

We perform a lattice investigation of QCD with three colors and 2 flavors of Dirac (staggered) fermions in the adjoint representation, defined on a 4d space with one spatial dimension compactified, and study the phase structure of the theory as a function of the size Lc of the compactified dimension. We show that four different phases take place, corresponding to different realizations of center symmetry: two center symmetric phases, for large or small values of Lc, separated by two phases in which center symmetry is broken in two different ways; the dependence of these results on the quark mass is discussed. We study also chiral properties and how they are affected by the different realizations of center symmetry; chiral symmetry, in particular, stays spontaneously broken at the phase transitions and may be restored at much lower values of the compactification radius. Our results could be relevant to a recently proposed conjecture of volume indepedence of QCD with adjoint fermions in the large Nc limit.