Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops

TL;DR

This paper demonstrates how certain 1/8 BPS Wilson loops in four-dimensional N=4 super Yang-Mills theory on a sphere can be computed using a two-dimensional constrained Higgs-Yang-Mills theory, supporting a recent conjecture.

Contribution

It establishes a localization framework from 4d N=4 SYM to 2d cHYM theory for specific Wilson loops, confirming the conjectured relation.

Findings

Expectation values of Wilson loops are captured by 2d cHYM theory.

Agreement with the bosonic Yang-Mills prescription excluding instantons.

Supports the conjecture by Drukker et al. on Wilson loops in N=4 SYM.

Abstract

We localize the four-dimensional N=4 super Yang-Mills theory on a four-sphere to the two-dimensional constrained Hitchin/Higgs-Yang-Mills (cHYM) theory on a two-sphere S^2. We show that expectation values of certain 1/8 BPS supersymmetric Wilson loops on S^2 in the 4d N=4 SYM is captured by the 2d cHYM theory. We further argue that expectation values of Wilson loops in the cHYM theory agree with the prescription "two-dimensional bosonic Yang-Mills excluding instanton contributions". Hence, we support the recent conjecture by Drukker, Giombi, Ricci and Trancanelli on the 1/8 BPS Wilson loops on S^2 in the 4d N=4 SYM.