On Crossing Symmmetry and Modular Invariance in Conformal Field Theory and S Duality in Gauge Theory

Abstract

In this note, we explore the relation between crossing symmetry and modular invariance in conformal field theory and S-duality in gauge theory. It is shown that partition functions of different S dual theories of N=2 SU(2) gauge theory with four fundamentals can be derived from the crossing symmetry of the Liouville four point function. We also show that the partition function of N=4 SU(2) gauge theory can be derived from the Liouville partition function on torus.

5 pages, 4 figures

References in corpus (7)

• S-duality in N=2 supersymmetric gauge theories
• Webs of five-branes and N=2 superconformal field theories
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• Loop operators and S-duality from curves on Riemann surfaces
• New Seiberg Dualities from N=2 Dualities
• N=2 SU Quiver with USP Ends or SU Ends with Antisymmetric Matter
• Supercriticality of a Class of Critical String Cosmological Solutions

Cited by in corpus (32)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• S-duality and 2d Topological QFT
• On non-conformal limit of the AGT relations
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• The Quiver Matrix Model and 2d-4d Conformal Connection
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• Hitchin systems, N=2 gauge theories and W-gravity
• Proving AGT conjecture as HS duality: extension to five dimensions
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• Proving AGT relations in the large-c limit
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Non-conformal limit of AGT relation from the 1-point torus conformal block
• Towards a proof of AGT conjecture by methods of matrix models
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Check of AGT Relation for Conformal Blocks on Sphere
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• N=2 Generalized Superconformal Quiver Gauge Theory
• From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• A Note on Wilson Loop in N=2 Quiver/M theory Gravity Duality