Weak-coupling analysis of the single-site large-N gauge theory coupled to adjoint fermions

TL;DR

This paper analyzes the weak-coupling behavior of a single-site large-N gauge theory with adjoint fermions, demonstrating conditions under which the continuum limit can be recovered using a four-dimensional eigenvalue density approach.

Contribution

It extends the weak-coupling analysis to real fermion flavors and supports the continuum limit recovery with a novel eigenvalue density method.

Findings

Continuum limit achievable for certain fermion flavors with zero bare mass

Eigenvalue density function effectively describes eigenvalue distribution

Analysis supports extension to real fermion flavor numbers

Abstract

We consider the leading-order expression at weak-coupling for a single-site large-N gauge theory coupled to adjoint fermions. We study the case of overlap and wilson fermions. We extend the theory to real values of the number of fermion flavors and restrict ourselves to asymptotically free theories. Using a four-dimensional density function for the distribution of the eigenvalues of the link variables, we show that it is possible to recover the infinite-volume continuum limit for a certain range of fermion flavors if we use fermions with a bare mass of zero. Our use of the four-dimensional density function is supported by a direct analysis of the lattice action.