Large-N volume reduction of lattice QCD with adjoint Wilson fermions at weak-coupling

Abstract

We study the large-N volume reduction of QCD with adjoint quarks regularized on the lattice. Specifically, we use Wilson fermions, and while our d-dimensional lattice has (d-1) infinite dimensions, the remaining direction is reduced to a point. We perform a weak-coupling one-loop calculation of the free energy as a function of the holonomy in the reduced direction, and map the regimes in the bare lattice parameter space where the holonomy averages to zero and a Z_N-center symmetric configuration is the ground state. For d=4 and N_f=1/2,1 and 2 Dirac flavors we see that the center symmetry is intact in a generous regime of the phase diagram that includes the chiral point. Thus we see that large-N volume independence of lattice QCD with adjoint Wilson quarks works at weak coupling. Interestingly, we find that this is true even if the quark mass is quite large, and this opens a path to study the volume reduced large-N pure gauge theory. Finally, we analyze in detail the UV sensitivity of the one-loop potential and show that treating the reduced theory as a (d-1)-dimensional effective field theory requires the introduction of certain relevant operators that are a subset of those suggested by Unsal and Yaffe to stabilize the center symmetry. This means that different regularizations of the volume-reduced theory can be compared only if one includes these terms in the action.