Modular bootstrap in Liouville field theory

Abstract

The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.

11 pages

References in corpus (6)

• Recursion relations in CFT and N=2 SYM theory
• Recursive representation of the torus 1-point conformal block
• H^+_3 WZNW model from Liouville field theory
• Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
• Analytic continuation formulae for the BPZ conformal block
• Recent progress on Liouville Field Theory

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