Structure Constants in the $N=1$ Super-Liouville Field Theory

TL;DR

This paper analyzes the structure constants of the N=1 Super-Liouville field theory, deriving explicit three-point functions in different sectors by solving differential and functional equations rooted in superconformal symmetry.

Contribution

It provides explicit formulas for three-point correlation functions in N=1 Super-Liouville theory, extending understanding of its structure constants and symmetry properties.

Findings

Derived differential equations for correlation functions with degenerated fields.

Solved these equations using hypergeometric functions for four-point functions.

Obtained explicit three-point functions in Neveu-Schwarz and Ramond sectors.

Abstract

The symmetry algebra of $N=1$ Super-Liouville field theory in two dimensions is the infinite dimensional $N=1$ superconformal algebra, which allows one to prove, that correlation functions, containing degenerated fields obey some partial linear differential equations. In the special case of four point function, including a primary field degenerated at the first level, this differential equations can be solved via hypergeometric functions. Taking into account mutual locality properties of fields and investigating s- and t- channel singularities we obtain some functional relations for three- point correlation functions. Solving this functional equations we obtain three-point functions in both Neveu-Schwarz and Ramond sectors.