Gravitational Yang-Lee Model. Four Point Function

TL;DR

This paper numerically evaluates the four-point function in the gravitational Yang-Lee model, introduces an effective integration method, discusses the classical limit, and conjectures an explicit partition function at a special solvable point.

Contribution

It provides a novel numerical approach for the four-point function and proposes an explicit expression at a specific solvable point in the gravitational Yang-Lee model.

Findings

Numerical evaluation of the four-point perturbative contribution.

Effective elliptic parameterization of the moduli space for integration.

Conjectured explicit partition function at the second solvable point.

Abstract

The four-point perturbative contribution to the spherical partition function of the gravitational Yang-Lee model is evaluated numerically. An effective integration procedure is due to a convenient elliptic parameterization of the moduli space. At certain values of the ``spectator'' parameter the Liouville four-point function involves a number of ``discrete terms'' which have to be taken into account separately. The classical limit, where only discrete terms contribute, is also discussed. In addition, we conjecture an explicit expression for this partition function at the ``second solvable point'' where the spectator matter is in fact another $M_{2/5}$ (Yang-Lee) minimal model.