Quantum Inverse Scattering Method and (Super)Conformal Field Theory

TL;DR

This paper explores applying the quantum inverse scattering method to superconformal field theory and its integrable perturbations, focusing on the quantum $ ext{osp}(1|2)$ super-KdV hierarchy and deriving fusion relations for transfer-matrices.

Contribution

It introduces the quantum monodromy matrix for superconformal theories and derives fusion relations using explicit irreducible representations of $ ext{osp}_q(1|2)$.

Findings

Quantum monodromy matrix constructed for superconformal field theory.

Fusion relations for transfer-matrices derived from $ ext{osp}_q(1|2)$ representations.

Connection established between classical super-KdV hierarchy and quantum inverse scattering.

Abstract

In this paper we consider the possibility of application of the quantum inverse scattering method for studying the superconformal field theory and it's integrable perturbations. The classical limit of the considered constructions is based on $\hat{osp}(1|2)$ super-KdV hierarchy. The quantum counterpart of the monodromy matrix corresponding to the linear problem associated with the L-operator is introduced. Using the explicit form of the irreducible representations of $\hat{osp}_q(1|2)$, the ``fusion relations'' for the transfer-matrices (i.e. the traces of the monodromy matrices in different representations) are obtained.