Partial breakdown of center symmetry in large-N QCD with adjoint Wilson fermions

TL;DR

This paper analyzes the phase structure of large-N QCD with adjoint Wilson fermions on a discretized space-time, revealing a cascade of symmetry-breaking transitions influenced by fermion mass and lattice anisotropy.

Contribution

It extends previous one-loop potential results to include lattice anisotropy and demonstrates a cascade of Z_N symmetry-breaking transitions as fermion mass varies.

Findings

For 0<xi<2, the minimum of the potential is Z_N symmetric at the chiral point.

A cascade of Z_N to Z_K symmetry-breaking transitions occurs as fermion mass increases.

The phase structure aligns with continuum results despite UV sensitivities.

Abstract

We study the one-loop potential of large-N QCD with adjoint Dirac fermions. Space-time is a discretization of R^3 x S^1 where the compact direction consists of a single lattice site. We use Wilson fermions with different values of the quark mass m and set the lattice spacings in the compact and non-compact directions to be a_t and a_s respectively. Extending the results of JHEP 0906:091,2009, we prove that if the ratio xi = a_s/a_t obeys 0<xi<2, then the minimum of the one-loop lattice potential for one or more Dirac flavors is Z_N symmetric at the chiral point. For xi=0 our formulas reduce to those obtained in a continuum regularization of the R^3, and our proof holds in that case as well. As we increase m from zero, we find a cascade of transitions where Z_N breaks to Z_K. For very small masses, K ~ 1/(a_t m) >> 1, while for large masses K ~ O(1). Despite certain UV sensitivities of the lattice one-loop potential, this phase structure is similar to the one obtained in the continuum works of Kovtun-Unsal-Yaffe, Myers-Ogilvie, and Hollowood-Myers. We explain the physical origin of the cascade of transitions and its relation to the embedding of space-time into color space.