Exact beta function and glueball spectrum in large-N Yang Mills theory

TL;DR

This paper derives an exact beta function and glueball spectrum for a solvable quasi-BPS sector in large-N Yang-Mills theory using a novel holomorphic loop equation, drawing analogies with supersymmetric gauge theories.

Contribution

It introduces a new holomorphic loop equation for quasi-BPS Wilson loops, enabling exact solutions in a non-supersymmetric large-N Yang-Mills sector.

Findings

Exact beta function for the quasi-BPS sector

Explicit glueball spectrum in the large-N limit

Development of a localized holomorphic loop equation

Abstract

In the pure large-N Yang-Mills theory there is a quasi-BPS sector that is exactly solvable at large N. It follows an exact beta function and the glueball spectrum in this sector. The main technical tool is a new holomorphic loop equation for quasi-BPS Wilson loops, that occurs as a non-supersymmetric analogue of Dijkgraaf-Vafa holomorphic loop equation for the glueball superpotential of n=1 SUSY gauge theories. The new holomorphic loop equation is localized, i.e. reduced to a critical equation, by a deformation of the loop that is a vanishing boundary in homology, somehow in analogy with Witten's cohomological localization by a coboundary deformation in SUSY gauge theories.