S-duality and 2d topological QFT View Full Text


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Article Info

DATE

2010-03

AUTHORS

Abhijit Gadde, Elli Pomoni, Leonardo Rastelli, Shlomo S. Razamat

ABSTRACT

We study the superconformal index for the class of 4d superconformal field theories recently introduced by Gaiotto [1]. 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 A1 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 [2]. More... »

PAGES

32

References to SciGraph publications

  • 2009-12-10. Recursion relations in CFT and N=2 SYM theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-10. An Index for 4 Dimensional Super Conformal Theories in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2010-02. Liouville Correlation Functions from Four-Dimensional Gauge Theories in LETTERS IN MATHEMATICAL PHYSICS
  • 2009-09-18. New Seiberg dualities from 𝒩 = 2 dualities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-11-04. AN−1 conformal Toda field theory correlation functions from conformal 𝒩 = 2 SU(N) quiver gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-07-20. Six-dimensional DN theory and four-dimensional SO-USp quivers in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01. Loop and surface operators in gauge theory and Liouville modular geometry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-08-27. N = 2 SU quiver with USP ends or SU ends with antisymmetric matter in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-09-09. Webs of five-branes and 𝒩 = 2 superconformal field theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-11-10. Zamolodchikov asymptotic formula and instanton expansion in 𝒩 = 2 SUSY Nf = 2Nc QCD in JOURNAL OF HIGH ENERGY PHYSICS
  • 1988-01. Topological quantum field theories in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 2010-02. Gauge theory loop operators and Liouville theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-09-03. Loop operators and S-duality from curves on Riemann surfaces in JOURNAL OF HIGH ENERGY PHYSICS
  • Journal

    TITLE

    Journal of High Energy Physics

    ISSUE

    3

    VOLUME

    2010

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/jhep03(2010)032

    DOI

    http://dx.doi.org/10.1007/jhep03(2010)032

    DIMENSIONS

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