Four-point function in Super Liouville Gravity

TL;DR

This paper analyzes four-point functions in super Liouville gravity coupled with minimal superconformal theory, providing explicit formulas and methods for calculating correlation numbers, especially focusing on boundary contributions involving logarithmic fields.

Contribution

It introduces a method to evaluate four-point correlation functions in super Liouville gravity, utilizing boundary terms and logarithmic fields, extending techniques from the bosonic case.

Findings

Explicit three-point correlation numbers provided

Boundary term reduction for four-point functions demonstrated

Construction and operator product expansions of logarithmic fields analyzed

Abstract

We consider the 2D super Liouville gravity coupled to the minimal superconformal theory. We analyze the physical states in the theory and give the general form of the n-point correlation numbers on the sphere in terms of integrals over the moduli space. The three-point correlation numbers are presented explicitly. For the four-point correlators, we show that the integral over the moduli space reduces to the boundary terms if one of the fields is degenerate. It turns out that special logarithmic fields are relevant for evaluating these boundary terms. We discuss the construction of these fields and study their operator product expansions. This analysis allows evaluating the four-point correlation numbers. The derivation is analogous to the one in the bosonic case and is based on the recently derived higher equations of motion of the super Liouville field theory.