A 4D-2D equivalence for large-N Yang-Mills theory

TL;DR

This paper demonstrates that the spectrum of large-N 4D pure Yang-Mills theory compactified on a small three-sphere matches that of a 2D irrational conformal field theory, providing evidence for a duality.

Contribution

It explicitly shows a 4D-2D equivalence for large-N Yang-Mills theory in a specific compactification limit, supporting string-theoretic duality conjectures.

Findings

Confined-phase spectrum matches 2D CFT spectrum

Supports 4D-2D duality in non-supersymmetric theories

Provides a solvable limit for large-N Yang-Mills analysis

Abstract

General string-theoretic considerations suggest that four-dimensional large-N gauge theories should have dual descriptions in terms of two-dimensional conformal field theories. However, for non-supersymmetric confining theories such as pure Yang-Mills theory, a long-standing challenge has been to explicitly show that such dual descriptions actually exist. In this paper, we consider the large-N limit of four-dimensional pure Yang-Mills theory compactified on a three-sphere in the solvable limit where the sphere radius is small compared to the strong length scale, and demonstrate that the confined-phase spectrum of this gauge theory coincides with the spectrum of an irrational two-dimensional conformal field theory.