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

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.

63 pages, phyzzx

References in corpus (3)

• Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level
• On the free field realization of the osp(1|2) current algebra
• Structure constants for the osp(1|2) current algebra

Cited by in corpus (8)

• Integrable quantum field theories with OSP(m/2n) symmetries
• Integrable quantum field theories with supergroup symmetries: the $OSP(1/2)$ case
• An admissible level $\widehat{\mathfrak{osp}}\left(1|2\right)$-model: modular transformations and the Verlinde formula
• Graded Parafermions
• Admissible level $\mathfrak{osp}(1|2)$ minimal models and their relaxed highest weight modules
• Modular Transformations and Invariants in the Context of Fractional Level Affine sl(2|1;C)
• N-point and higher-genus osp(1|2) fusion
• Explicit Decompositions of Weyl Reflections in Affine Lie Algebras