Structure constants for the osp(1|2) current algebra

TL;DR

This paper derives structure constants and fusion rules for the osp(1|2) current algebra using free field realization and Coulomb gas techniques, linking it to N=1 superconformal theories.

Contribution

It provides explicit integral representations for conformal blocks and calculates structure constants for osp(1|2) current algebra at positive integer levels.

Findings

Explicit integral formulas for conformal blocks

Derived structure constants for primary operators

Established connections to N=1 superconformal theories

Abstract

We study the free field realization of the two-dimensional osp(1|2) current algebra. We consider the case in which the level of the affine osp(1|2) symmetry is a positive integer. Using the Coulomb gas technique we obtain integral representations for the conformal blocks of the model. In particular, from the behaviour of the four-point function, we extract the structure constants for the product of two arbitrary primary operators of the theory. From this result we derive the fusion rules of the osp(1|2) conformal field theory and we explore the connections between the osp(1|2) affine symmetry and the N=1 superconformal field theories.