S-duality and 2d Topological QFT

Oct, 2009
25 pages
Published in:
  • JHEP 03 (2010) 032
e-Print:
Report number:
  • YITP-SB-09-30

Citations per year

2009201320172021202405101520
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