Four-point correlation numbers in super Minimal Liouville Gravity in the Ramond sector

TL;DR

This paper derives a closed-form analytic expression for four-point correlation numbers in super Minimal Liouville Gravity's Ramond sector, extending previous work on three-point functions and utilizing higher equations of motion.

Contribution

It introduces a novel analytic method to compute four-point correlation numbers in the Ramond sector of super Minimal Liouville Gravity, building on prior three-point function evaluations.

Findings

Derived a closed-form expression for four-point correlation numbers.

Extended the higher equations of motion approach to the Ramond sector.

Connected four-point functions with boundary contributions from OPE structures.

Abstract

In this work, we continue the investigation of correlation numbers in $\mathcal{N}=1$ super Minimal Liouville Gravity (SMLG), with physical fields in the Ramond sector. Building upon our previous construction of physical operators and the evaluation of three-point correlation functions involving Ramond and Neveu-Schwarz (NS) insertions, we now turn to the analytic computation of four-point correlation numbers. This development is motivated by the framework established for the bosonic Minimal Liouville Gravity and its supersymmetric NS analog, where the integration over moduli space in correlation functions can be performed explicitly using the higher equations of motion (HEM) in Liouville theory. In particular, if one of the insertions corresponds to a degenerate field, the four-point amplitude can be expressed in terms of boundary contributions obtained from the OPE structure of logarithmic counterparts of ground ring elements. We aim to adapt and generalize this approach to the Ramond sector.Our result is a closed-form analytic expression for four-point correlation numbers involving Ramond fields.