On construction of correlation numbers in super Minimal Liouville Gravity in the Ramond sector

TL;DR

This paper develops a method to compute correlation numbers involving Ramond sector fields in super minimal Liouville gravity, including constructing physical fields and establishing their relation to the ground ring, enabling explicit calculations.

Contribution

It introduces a new representation of Ramond physical fields and a direct analytic method for computing their correlation numbers in super Liouville theory.

Findings

Constructed Ramond sector physical fields.

Derived a relation between Ramond fields and the ground ring.

Demonstrated explicit three-point correlation computation.

Abstract

We study the construction of correlation numbers in super minimal Liouville gravity. In particular, we construct the fundamental physical fields in the Ramond sector and compute the three-point correlation number involving two physical fields in the Ramond sector and one in the NS sector. Furthermore, we establish the relation between Ramond physical fields and the elements of the ground ring. Using the higher equations of motion of super Liouville theory, this relation leads to a new representation of the Ramond physical fields. This formulation enables a direct analytic computation of correlation numbers involving Ramond field insertions. As an application, we demonstrate the method in the simplest case of a three-point correlation function.