On the Liouville coupling constants

Abstract

For the general operator product algebra coefficients derived by Cremmer Roussel Schnittger and the present author with (positive integer) screening numbers, the coupling constants determine the factors additional to the quantum group 6j symbols. They are given by path independent products over a two dimensional lattice in the zero mode space. It is shown that the ansatz for the three point function of Dorn-Otto and Zamolodchikov-Zamolodchikov precisely defines the corresponding flat lattice connection, so that it does give a natural generalization of these coupling constants to continuous screening numbers. The consistency of the restriction to integer screening charges is reviewed, and shown to be linked with the orthogonality of the (generalized) 6j symbols. Thus extending this last relation is the key to general screening numbers.

Final version to be published in Phys. Lett. B

References in corpus (8)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Two and three-point functions in Liouville theory
• On Correlation Functions for Non-critical Strings with c<1 but d>1
• Gravity-Matter Couplings from Liouville Theory
• Solving the Strongly Coupled 2D Gravity: 2. Fractional-Spin Operators, and Topological Three-Point Functions
• The Braiding of Chiral Vertex Operators with Continuous Spins in 2D Gravity
• Continous Spins in 2D Gravity: Chiral Vertex Operators and Local Fields
• The Quantum Group Structure of 2D Gravity and Minimal Models II: The Genus-Zero Chiral Bootstrap

Cited by in corpus (3)

• Liouville Field Theory -- A decade after the revolution
• Negative Screenings in Liouville Theory
• On a relation between Liouville field theory and a two component scalar field theory passing through the random walk