Recent progress on Liouville Field Theory

TL;DR

This paper presents an explicit construction of Liouville conformal blocks' monodromy using quantum group Racah-Wigner coefficients, proving crossing-symmetry and deriving boundary correlator expressions.

Contribution

It introduces a novel explicit construction linking Liouville conformal blocks with quantum group coefficients, establishing crossing-symmetry analytically.

Findings

Crossing-symmetry for four-point functions proven analytically

Explicit expression for three boundary operators' correlator derived

Monodromy of conformal blocks expressed via Racah-Wigner coefficients

Abstract

An explicit construction for the monodromy of the Liouville conformal blocks in terms of Racah-Wigner coefficients of the quantum group U_q(sl(2,R)) is proposed. As a consequence, crossing-symmetry for four point functions is analytically proven, and the expression for the correlator of three boundary operators is obtained.