Yang-Mills Integrals for Orthogonal, Symplectic and Exceptional Groups

TL;DR

This paper investigates Yang-Mills integrals for various gauge groups using numerical and analytic methods, revealing discrepancies with previous results and providing new insights into their convergence and properties.

Contribution

It extends the analysis of Yang-Mills integrals to orthogonal, symplectic, and exceptional groups, employing Monte Carlo and deformation techniques for the first time in this context.

Findings

Numerical results differ from earlier studies.

Deformation method shows excellent agreement with simulations.

Convergence properties of bosonic integrals are discussed.

Abstract

We apply numerical and analytic techniques to the study of Yang-Mills integrals with orthogonal, symplectic and exceptional gauge symmetries. The main focus is on the supersymmetric integrals, which correspond essentially to the bulk part of the Witten index for susy quantum mechanical gauge theory. We evaluate these integrals for D=4 and group rank up to three, using Monte Carlo methods. Our results are at variance with previous findings. We further compute the integrals with the deformation technique of Moore, Nekrasov and Shatashvili, which we adapt to the groups under study. Excellent agreement with all our numerical calculations is obtained. We also discuss the convergence properties of the purely bosonic integrals.