Semiclassical limit of the FZZT Liouville theory

TL;DR

This paper analyzes the semiclassical limit of FZZT Liouville theory on the upper half plane, proving the Polyakov conjecture and calculating classical actions for various operator configurations, aligning with quantum correlators.

Contribution

It proves the Polyakov conjecture for the classical Liouville action and computes it for multiple operator configurations in FZZT Liouville theory.

Findings

The classical Liouville action matches the quantum correlator limits.

The Polyakov conjecture is validated in this context.

Explicit calculations of the classical action for different operator setups.

Abstract

The semiclassical limit of the FZZT Liouville theory on the upper half plane with bulk operators of arbitrary type and with elliptic boundary operators is analyzed. We prove the Polyakov conjecture for an appropriate classical Liouville action. This action is calculated in a number of cases: one bulk operator of arbitrary type, one bulk and one boundary, and two boundary elliptic operators. The results are in agreement with the classical limits of the corresponding quantum correlators.