Connecting Localization and Wall-Crossing via D-Branes

TL;DR

This paper links the computation of BPS line operator vevs in 4d N=2 super Yang-Mills theory to Darboux coordinates, refining the expansion with monopole bubbling contributions derived from D-brane realizations.

Contribution

It explicitly connects localization results with Darboux coordinate expansions and introduces monopole bubbling contributions via D-brane methods for precise line operator vev calculations.

Findings

Refined the expansion of line operator vevs with monopole bubbling contributions.

Derived and incorporated monopole bubbling effects from D-brane realizations.

Predicted degeneracies of framed BPS states contributing to line operators.

Abstract

We demonstrate explicitly that the vacuum expectation values (vevs) of BPS line operators in 4d N=2 super Yang-Mills theory compactified on a circle, computed by localization techniques, can be expanded in terms of Darboux coordinates as proposed by Gaiotto, Moore, and Neitzke [arXiv:1006.0146]. However, we need to refine the expansion by including additional novel monopole bubbling contributions to obtain a precise match. Using D-brane realization of these singular BPS line operators, we derive and incorporate the monopole bubbling contributions as well as predict the degeneracies of framed BPS states contributing to the line operator vevs in the limit of vanishing simultaneous spatial and R-symmetry rotation fugacity parameter.