Correlation Functions in non critical (super) string theory

TL;DR

This paper computes correlation functions of the super Liouville theory coupled to matter fields on spherical worldsheets, extending methods from bosonic theories and providing closed-form results for tachyon vertex operators.

Contribution

It introduces a method to compute super Liouville correlation functions with arbitrary screening charges, generalizing known bosonic results to the supersymmetric case.

Findings

Derived closed-form expressions for super Liouville correlators.

Showed the parallel between super and bosonic correlation functions.

Included arbitrary screening charges in the calculation.

Abstract

We consider the correlation functions of the tachyon vertex operator of the super Liouville theory coupled to matter fields in the super Coulomb gas formulation, on world sheets with spherical topology. After integrating over the zero mode and assuming that the $s$ parameter takes an integer value, we subsequently continue it to an arbitrary real number and compute the correlators in a closed form. We also included an arbitrary number of screening charges and, as a result, after renormalizing them, as well as the external legs and the cosmological constant, the form of the final amplitudes do not modify. The result is remarkably parallel to the bosonic case. For completeness, we discussed the calculation of bosonic correlators including arbitrary screening charges.