Phase diagram of adjoint QCD at weak coupling and finite volume

TL;DR

This paper analyzes the phase diagram of adjoint QCD on finite volume manifolds at weak coupling, revealing conditions for confinement and deconfinement phases, with implications for large N volume reduction and comparison to lattice data.

Contribution

It provides the first large N phase diagram of adjoint QCD on S^1 x S^3 at weak coupling, including the critical mass-radius relation for confinement.

Findings

Confined phase favored for light adjoint fermions below a critical mass-radius product.

Phase diagram matches lattice results for N=3.

Supports large N volume reduction in certain parameter regimes.

Abstract

The phase diagram of SU(N) gauge theories with fermions in an arbitrary representation R can be calculated on finite volume manifolds such as S^1 x S^3. When S^3 is small a perturbative analysis is possible and the weak-coupling analogue of the pure Yang-Mills theory confinement-deconfinement transition is accessible in the large N limit. We calculate the large N phase diagram of adjoint QCD [SU(N) gauge theory with adjoint fermions] where periodic boundary conditions are applied to fermions on S^1 such that the confined phase is favored for light enough adjoint fermion mass. We calculate the value of the mass times the radius of S^3 below which the confined phase is favored for all volumes of S^1 / S^3 and discuss the implications for large N volume reduction. We calculate also the phase diagram for N = 3 and compare with recent lattice results.