Integrable Structure of Superconformal Field Theory and Quantum super-KdV Theory

TL;DR

This paper explores the integrable structure of 2D superconformal field theory, connecting classical super-KdV hierarchy with quantum monodromy matrices, fusion relations, and supersymmetric Toda field theory.

Contribution

It introduces the quantum monodromy matrix for superconformal field theory and derives fusion relations for transfer matrices in the quantum superalgebra context.

Findings

Derived fusion relations for transfer matrices in $ ext{osp}_q(1|2)$

Classified integrable perturbations and their operators

Linked superconformal field theory with supersymmetric Toda models

Abstract

The integrable structure of the two dimensional superconformal field theory is considered. The classical counterpart of our constructions is based on the $\hat{osp}(1|2)$ super-KdV hierarchy. The quantum version of the monodromy matrix associated with the linear problem for the corresponding L-operator is introduced. Using the explicit form of the irreducible representations of $\hat{osp}_q(1|2)$, the so-called "fusion relations" for the transfer matrices considered in different representations of $\hat{osp}_q(1|2)$ are obtained. The possible integrable perturbations of the model (primary operators, commuting with integrals of motion) are classified and the relation with the supersymmetric $\hat{osp}(1|2)$ Toda field theory is discussed.