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Holomorphic reduction of N = 2 gauge theories, Wilson-'t Hooft operators, and S-duality

Kapustin, Anton (2006) Holomorphic reduction of N = 2 gauge theories, Wilson-'t Hooft operators, and S-duality. . (Submitted)

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We study twisted N=2 superconformal gauge theory on a product of two Riemann surfaces Sigma and C. The twisted theory is topological along C and holomorphic along Sigma and does not depend on the gauge coupling or theta-angle. Upon Kaluza-Klein reduction along Sigma, it becomes equivalent to a topological B-model on C whose target is the moduli space MV of nonabelian vortex equations on Sigma. The N=2 S-duality conjecture implies that the duality group acts by autoequivalences on the derived category of MV. This statement can be regarded as an N=2 counterpart of the geometric Langlands duality. We show that the twisted theory admits Wilson-'t Hooft loop operators labelled by both electric and magnetic weights. Correlators of these loop operators depend holomorphically on coordinates and are independent of the gauge coupling. Thus the twisted theory provides a convenient framework for studying the Operator Product Expansion of general Wilson-'t Hooft loop operators.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Additional Information:I would like to thank D. Arinkin, R. Bezrukavnikov, I. Mirkovic, and N. Hitchin for explanations and discussions, and S. Gukov, N. Hitchin, and N. Saulina for comments on the preliminary draft of the paper. I am also grateful to Ketan Vyas for performing some computations related to the discussion of OPE of Wilson and ’t Hooft operators in section 4.2. This work was supported in part by the DOE grant DE-FG03-92-ER40701.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-92-ER40701
Record Number:CaltechAUTHORS:20160511-100705968
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66983
Deposited By: Tony Diaz
Deposited On:11 May 2016 17:13
Last Modified:03 Oct 2019 10:01

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