Loop operators and S-duality from curves on Riemann surfaces

Details Loop operators and S-duality from curves on Riemann surfaces Loop operators and S-duality from curves on Riemann surfaces

2009-07-15

arxiv.org/abs/0907.2593v1

JHEP 0909:031,2009

Physics

High Energy Physics

High Energy Physics - Theory

41 pages

Scientific paper

10.1088/1126-6708/2009/09/031

We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We then show that this precisely matches Dehn's classification of homotopy classes of non-self-intersecting curves on an associated Riemann surface--the same surface which characterizes the gauge theory. Our analysis provides an explicit prediction for the action of S-duality on loop operators in these theories which we check against the known duality transformation in several examples.

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