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

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.