Quantization of the N=2 Supersymmetric KdV Hierarchy

TL;DR

This paper advances the understanding of quantizing N=2 supersymmetric KdV hierarchies by introducing a novel algebraic construction for the L-operator and demonstrating the invariance of the transfer matrix under supersymmetry.

Contribution

It presents a new algebraic approach to the L-operator for the N=2 supersymmetric KdV hierarchy and constructs a quantum monodromy matrix satisfying a reflection equation.

Findings

Quantum monodromy matrix constructed for N=2 supersymmetric KdV.

Transfer matrix invariant under supersymmetry transformations.

Classical limit recovers the known monodromy matrix.

Abstract

We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based on the $sl^{(1)}(2|1)$ affine algebra but with a new algebraic construction for the L-operator, different from the standard Drinfeld-Sokolov reduction. We construct the quantum monodromy matrix satisfying a special version of the reflection equation and show that in the classical limit, this object gives the monodromy matrix of N=2 supersymmetric KdV system. We also show that at both the classical and the quantum levels, the trace of the monodromy matrix (transfer matrix) is invariant under two supersymmetry transformations and the zero mode of the associated U(1) current.