Large-N reduction with two adjoint Dirac fermions

TL;DR

This paper investigates the phase structure of a single-site SU(N) gauge theory with two adjoint Wilson fermions, analyzing symmetry breaking and potential extraction at large N up to 53, to understand large-N reduction.

Contribution

It provides the phase diagram of the theory at large N, identifying regions with unbroken center symmetry and exploring the feasibility of extracting the heavy-quark potential.

Findings

Unbroken center symmetry found near critical kappa values for N up to 53.

Heavy-quark potential can be extracted at small distances with N <= 53.

Long-distance potential extraction requires larger N or more lattice sites.

Abstract

We study the single site SU(N) lattice gauge theory with N_f=2 adjoint Wilson fermions for values of N up to 53. We determine the phase diagram of the theory as a function of the hopping parameter kappa and the inverse 't Hooft coupling b, searching for the region in which the Z_N^4 center symmetry is unbroken. In this region the theory is equivalent to the infinite volume theory when N goes to infinity. We find a region of values of kappa on both sides of kappa_c for which the symmetry is unbroken, including both light physical quarks and masses ~O(1/a). This is surrounded by a region with a complicated sequence of partially broken phases. We calculate Wilson loop expectation values and find that using N <= 53 it is possible to extract the heavy-quark potential at small distances (1-3 links) but not at longer distances. For this, larger values of N, or lattices with more sites, are needed.