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

TL;DR

This paper demonstrates that large-N volume reduction in lattice QCD with adjoint Wilson fermions remains valid at weak coupling, even with heavy quarks, by analyzing the center symmetry and UV sensitivities through one-loop calculations.

Contribution

It provides a detailed one-loop analysis of the holonomy and center symmetry in lattice QCD with adjoint Wilson fermions, confirming volume independence at weak coupling and clarifying UV effects.

Findings

Center symmetry remains intact in a broad phase diagram region.

Large-N volume reduction is valid even with heavy quarks.

UV sensitivity requires specific relevant operators for stabilization.

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.