Holomorphic reduction of N = 2 gauge theories, Wilson-'t Hooft operators, and S-duality
By A. Kapustin. 2006
142 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/8cf996e280cdee39efe86d839b6062fcf7051754
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Citations in the corpus
- Loop operators and S-duality from curves on Riemann surfaces (2009, background): “As for the transformations of the loop operators, in the case where the nondynamical gauge fields are turned off, this problem was studied in [17].”
- Framed BPS states (2010, unknown): “For such theories we can be more specific about the definition of the line operators we are interested in following [18] and [20] (notice that our ζ is t−1 in the latter reference).”
- Supersymmetric gauge theory and the Yangian (2013, methodology): “nd d is of cohomological degree 1. Note that this is just a twist: no deformation is needed when there is at least N = 2 supersymmetry. The twist of the N = 2 gauge theory is that studied by Kapustin [Kap06]. These results can be verified using the techniques of [Cos11b], which relies heavily on the ”
- Electric-Magnetic Duality And The Geometric Langlands Program (2006, background): “It can be obtained as a reduction of a “holomorphic-topological” gauge theory on Σ × C [26].”
- Gauge theory loop operators and Liouville theory (2009, background): “Therefore, our proposal automatically incorporates the conjectured action of the S-duality group Γ(Tg,n) on gauge theory loop operators.”
- Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops (2007, unknown): “or Z1−loop with the partition function of instanton corrections |Zinst|2 in an arbitrary N= 2 superconformal case, integrate over aE and check predictions of the S-duality for these theories (see e.g.[53, 75]). 4.5. Example. Before turning to the instanton corrections, let us give a simplest example”
- Wall-crossing in coupled 2d-4d systems (2011, background): “The present paper together with [15, 16, 17] may be viewed as part of an analogous line of development for theories with N = 2 supersymmetry.”
- Two-dimensional SCFTs from wrapped branes and c-extremization (2013, methodology): “(14)Note that this N = (2, 2) SCFT is not the same as the N = (2, 2) SCFTs obtained in [40] by twisted compactifications of general four-dimensional N = 2 SCFTs on Riemann surfaces.”