On Field/String Theory Approach to Theta Dependence in Large N Yang-Mills Theory

TL;DR

This paper connects field theory and string theory approaches to understanding the theta dependence of vacuum energy in large N Yang-Mills theory, showing consistency and calculating corrections.

Contribution

It demonstrates that vacuum fluctuations in field theory match string theory results and computes 1/N corrections, reconciling both perspectives.

Findings

Vacuum energy from field theory aligns with string theory predictions.

Calculated 1/N suppressed corrections to the vacuum energy.

Revealed differences in vacuum stability for finite and infinite N.

Abstract

The theta dependence of the vacuum energy in large N Yang-Mills theory has been studied some time ago by Witten using a duality of large N gauge theories with string theory compactified on a certain space-time. We show that within the field theory context vacuum fluctuations of the topological charge give rise to the vacuum energy consistent with the string theory computation. Furthermore, we calculate 1/N suppressed corrections to the string theory result. The reconciliation of the string and field theory approaches is based on the fact that the gauge theory instantons carry zerobrane charge in the corresponding D-brane construction of Yang-Mills theory. Given the formula for the vacuum energy we study certain aspects of stability of the false vacua of the model for different realizations of the initial conditions. The vacuum structure appears to be different depending on whether N is infinite or, alternatively, large but finite.