Finite Volume Phases of Large N Gauge Theories with Massive Adjoint Fermions

TL;DR

This paper explores the phase structure of large N SU(N) gauge theories with massive adjoint fermions in a finite volume, revealing a rich variety of phases including confined, deconfined, and partially-confined states with multiple eigenvalue gaps.

Contribution

It introduces a detailed analysis of phase transitions and eigenvalue distributions in large N gauge theories with massive adjoint fermions on S^3 x S^1, extending understanding of phase structures beyond previous thermal studies.

Findings

Identifies a line of phase transitions between confined and deconfined phases for N_f=1.

Discovers multiple partially-confined phases with unbroken Z_p center symmetry for N_f>1.

Shows that for small fermion mass times radius, only the confined phase persists.

Abstract

The phase structure of QCD-like gauge theories with fermions in various representations is an interesting but generally analytically intractable problem. One way to ensure weak coupling is to define the theory in a small finite volume, in this case S^3 x S^1. Genuine phase transitions can then occur in the large N theory. Here, we use this technique to investigate SU(N) gauge theory with a number N_f of massive adjoint-valued Majorana fermions having non-thermal boundary conditions around S^1. For N_f =1 we find a line of transitions that separate the weak-coupling analogues of the confined and de-confined phases for which the density of eigenvalues of the Wilson line transform from the uniform distribution to a gapped distribution. However, the situation for N_f >1 is much richer and a series of weak-coupling analogues of partially-confined phases appear which leave unbroken a Z_p subgroup of the centre symmetry. In these Z_p phases the eigenvalue density has p gaps and they are separated from the confining phase and from one-another by first order phase transitions. We show that for small enough mR (the mass of the fermions times the radius of the S^3) only the confined phase exists. The large N phase diagram is consistent with the finite N result and with other approaches based on R^3 x S^1 calculations and lattice simulations.