Bootstrap in Supersymmetric Liouville Field Theory. I. NS Sector

TL;DR

This paper constructs and verifies four-point functions in N=1 supersymmetric Liouville theory's NS sector, introducing new recursion methods and a derivation based on singular vector decoupling, enhancing understanding of supersymmetric conformal blocks.

Contribution

It presents a new derivation of NS structure constants and introduces an elliptic recursion representation for NS blocks, staying within the NS sector without involving Ramond fields.

Findings

Successfully constructed four-point functions in the NS sector.

Verified bootstrap conditions numerically for various parameters.

Proposed a new recursion method for NS blocks.

Abstract

A four point function of basic Neveu-Schwarz exponential fields is constructed in the N = 1 supersymmetric Liouville field theory. Although the basic NS structure constants were known previously, we present a new derivation, based on a singular vector decoupling in the NS sector. This allows to stay completely inside the NS sector of the space of states, without referencing to the Ramond fields. The four-point construction involves also the NS blocks, for which we suggest a new recursion representation, the so-called elliptic one. The bootstrap conditions for this four point correlation function are verified numerically for different values of the parameters.