Large-N volume independence in conformal and confining gauge theories

TL;DR

This paper explores how large N gauge theories exhibit volume independence under certain conditions, allowing for simplified lattice studies and revealing phase structures in supersymmetric and QCD theories.

Contribution

It demonstrates that large N gauge theories maintain scale invariance and correlation lengths under compactification if center symmetry remains unbroken, extending volume independence to various theories.

Findings

Volume independence holds when center symmetry is unbroken.

Finite volume effects are suppressed by 1/N.

Lattice models can study phase boundaries with minimal volume.

Abstract

Consequences of large $N$ volume independence are examined in conformal and confining gauge theories. In the large $N$ limit, gauge theories compactified on $\R^{d-k} \times (S^1)^k$ are independent of the $S^1$ radii, provided the theory has unbroken center symmetry. In particular, this implies that a large $N$ gauge theory which, on $\R^d$, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on $\R^{d-k} \times (S^1)^k$. In other words, finite volume effects are $1/N$ suppressed. In lattice formulations of vector-like theories, this implies that numerical studies to determine the boundary between confined and conformal phases may be performed on one-site lattice models. In $N=4$ supersymmetric Yang-Mills theory, the center symmetry realization is a matter of choice: the theory on $\R^{4-k}\times (S^1)^k$ has a moduli space which contains points with all possible realizations of center symmetry. Large $N$ QCD with massive adjoint fermions and one or two compactified dimensions has a rich phase structure with an infinite number of phase transitions coalescing in the zero radius limit.