S-duality and 2d Topological QFT
Oct, 2009
25 pages
Published in:
- JHEP 03 (2010) 032
e-Print:
- 0910.2225 [hep-th]
Report number:
- YITP-SB-09-30
View in:
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Abstract: (arXiv)
We study the superconformal index for the class of N=2 4d superconformal field theories recently introduced by Gaiotto. These theories are defined by compactifying the (2,0) 6d theory on a Riemann surface with punctures. We interpret the index of the 4d theory associated to an n-punctured Riemann surface as the n-point correlation function of a 2d topological QFT living on the surface. Invariance of the index under generalized S-duality transformations (the mapping class group of the Riemann surface) translates into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for which the 4d SCFTs have a Lagrangian realization, the structure constants and metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma functions. Associativity then holds thanks to a remarkable symmetry of an elliptic hypergeometric beta integral, proved very recently by van de Bult.- Supersymmetric gauge theory
- Duality in Gauge Field Theories
- Topological Field Theories
- field theory: topological
- field theory: conformal
- S-duality: transformation
- operator: algebra
- correlation function
- compactification
- Riemann surface
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