Comments on large-N volume independence

TL;DR

This paper investigates the conditions under which large-N volume independence holds in Yang-Mills theories with adjoint fermions, revealing finite radiative corrections and the potential to study 4D physics via 3D effective theories.

Contribution

It identifies the critical lattice size for volume independence and shows that one-loop corrections are finite, enabling lower-dimensional analysis of 4D non-perturbative physics.

Findings

Critical lattice size for volume independence identified.

One-loop radiative corrections to Wilson-line masses are finite.

Volume independence can be maintained with parameter tuning even for G=1.

Abstract

We study aspects of the large-N volume independence on R**3 x L**G, where L**G is a G-site lattice for Yang-Mills theory with adjoint Wilson-fermions. We find the critical number of lattice sites above which the center-symmetry analysis on L**G agrees with the one on the continuum S**1. For Wilson parameter set to one and G>=2, the two analyses agree. One-loop radiative corrections to Wilson-line masses are finite, reminiscent of the UV-insensitivity of the Higgs mass in deconstruction/Little-Higgs theories. Even for theories with G=1, volume independence in QCD(adj) may be guaranteed to work by tuning one low-energy effective field theory parameter. Within the parameter space of the theory, at most three operators of the 3d effective field theory exhibit one-loop UV-sensitivity. This opens the analytical prospect to study 4d non-perturbative physics by using lower dimensional field theories (d=3, in our example).