Fusion rules and singular vectors of the osp(1|2) current algebra

TL;DR

This paper investigates the fusion rules and singular vectors of the osp(1|2) current algebra, revealing their structure and connections to superconformal models, advancing understanding of algebraic representations in theoretical physics.

Contribution

It introduces a new analysis of fusion rules and singular vectors for osp(1|2) current algebra, linking representation characters to superconformal models.

Findings

Derived fusion rules for admissible osp(1|2) representations.

Established relations between characters and superconformal models.

Developed equations for descendants of fused Verma modules.

Abstract

The fusion of Verma modules of the osp(1|2) current algebra is studied. In the framework of an isotopic formalism, the singular vector decoupling conditions are analyzed. The fusion rules corresponding to the admissible representations of the osp(1|2) algebra are determined. A relation between the characters of these last representations and those corresponding to the minimal superconformal models is found. A series of equations that relate the descendants of the highest weight vectors resulting from a fusion of Verma modules are obtained. Solving these equations the singular vectors of the theory can be determined.