Instantons and BPS Wilson loops

TL;DR

This work computes the one-instanton contribution to a circular BPS Wilson loop in ${ m 4}$-dimensional ${cal N}=4$ SU(2) Yang–Mills theory within the semiclassical framework. By exploiting residual symmetries, notably the $SO(2,2)$ conformal subgroup and an $OSp(2,2|4)$ fermionic invariance, the authors reduce the problem to integrating over eight bosonic and sixteen fermionic instanton moduli, organized via an $AdS_5$ interpretation of the instanton moduli space. After regulating boundary divergences associated with the AdS boundary, they obtain a finite, nonzero instanton contribution proportional to $e^{2π i τ}$ and $(g_{YM}^2/(8π^2))^4$, with no explicit dependence on the loop radius $R$, and with a clear ${ heta}_{YM}$-dependent phase. The results have implications for AdS/CFT, S-duality, and potential matrix-model connections, and the analysis suggests straightforward generalizations to ${ m SU}(N)$ and higher instanton numbers in the large-$N$ limit.

Abstract

The one-instanton contribution to a circular BPS Wilson loop in N=4 SU(2) Yang--Mills theory is evaluated in semiclassical approximation. This article amplifies part of a talk given by MBG at the Strings 2001 conference, Mumbai, India (January 5-10, 2001). The results are preliminary and a more complete exposition will be contained in a forthcoming paper.