Recursive representation of the torus 1-point conformal block

TL;DR

This paper derives a recursive relation for the torus 1-point conformal block, proves related identities, and demonstrates the method's efficiency through numerical analysis of modular invariance in Liouville theory.

Contribution

It introduces a recursive approach for the torus 1-point conformal block and verifies conjectured identities, enhancing computational techniques in conformal field theory.

Findings

Derived recursive relation for the 1-point conformal block on a torus

Proved identities between conformal blocks conjectured by Poghossian

Numerically confirmed the modular invariance of the 1-point Liouville correlation function

Abstract

The recursive relation for the 1-point conformal block on a torus is derived and used to prove the identities between conformal blocks recently conjectured by R. Poghossian. As an illustration of the efficiency of the recurrence method the modular invariance of the 1-point Liouville correlation function is numerically analyzed.