Quantum Liouville theory on the pseudosphere with heavy charges

TL;DR

This paper develops a perturbative approach to quantum Liouville theory on the pseudosphere with heavy charges, providing explicit calculations of correlation functions and confirming results with bootstrap methods.

Contribution

It introduces a perturbative expansion around heavy charge backgrounds and compares results with bootstrap approaches, demonstrating consistency and partial summation of conformal blocks.

Findings

Explicit one and two point function calculations

Agreement with Zamolodchikov bootstrap results

Partial summation of conformal blocks

Abstract

We develop a perturbative expansion of quantum Liouville theory on the pseudosphere around the background generated by heavy charges. Explicit results are presented for the one and two point functions corresponding to the summation of infinite classes of standard perturbative graphs. The results are compared to the one point function and to a special case of the two point function derived by Zamolodchikov and Zamolodchikov in the bootstrap approach, finding complete agreement. A partial summation of the conformal block is also obtained.