Moduli Space and Wall-Crossing Formulae in Higher-Rank Gauge Theories

Details Moduli Space and Wall-Crossing Formulae in Higher-Rank Gauge Theories Moduli Space and Wall-Crossing Formulae in Higher-Rank Gauge Theories

2011-05-23

arxiv.org/abs/1105.4584v1

JHEP 1111 (2011) 020

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, no figures

Scientific paper

10.1007/JHEP11(2011)020

We study the interplay between wall-crossing in four-dimensional gauge theory and instanton contributions to the moduli space metric of the same theory on $\mathbb{R}^{3}\times S^{1}$. We consider $\mathcal{N}=2$ SUSY Yang--Mills with gauge group SU(n) and focus on walls of marginal stability which extend to weak coupling. By comparison with explicit field theory results we verify the Kontsevich--Soibelman formula for the change in the BPS spectrum at these walls and check the smoothness of the metric in the corresponding compactified theory. We also verify in detail the predictions for the one instanton contribution to the metric coming from the non-linear integral equations of Gaiotto, Moore and Nietzke.

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