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

We study the one-loop potential of large-N QCD with adjoint Dirac fermions. Space-time is a discretization of R3 × S1 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 at and as respectively. Extending the results of JHEP 0906:091,2009, we prove that if the ratio ξ = as/at obeys 0 < ξ < 2, then the minimum of the one-loop lattice potential for one or more Dirac flavors is ZN symmetric at the chiral point. For ξ = 0 our formulas reduce to those obtained in a continuum regularization of the R3, and our proof holds in that case as well. As we increase m from zero, we find a cascade of transitions where ZN breaks to ZK. For very small masses, K ∼ 1/(atm) ≫ 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.