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 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 at and as 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 similar to 1/(a(t)m) >> 1, while for large masses K similar to 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.