Connecting localization and wall-crossing via D-branes
Chih-Kai Chang (Department of Physics, Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwan, Department of Physics, University of Chicago, Chicago, USA); Heng-Yu Chen (Department of Physics, Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwan); Dharmesh Jain (Department of Physics, Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwan, Theory Division, Saha Institute of Nuclear Physics, Kolkata, India)
; Norton Lee (Department of Physics and Astronomy, Stony Brook University, Stony Brook, USA, Department of Physics, Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwan)
We demonstrate explicitly that the vacuum expectation values (vevs) of BPS line operators in 4d 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 [1]. However, we need to augment the expressions for Darboux coordinates with additional 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.
