Supersymmetric WZW $\sigma$ Model on Full and Half Plane

TL;DR

This paper investigates the classical integrability of the supersymmetric U(N) sigma model with a Wess-Zumino-Witten term on full and half planes, demonstrating the existence of nonlocal conserved charges and their implications for integrability.

Contribution

It establishes the integrability of the supersymmetric WZW sigma model on both full and half planes by constructing conserved charges and analyzing boundary conditions.

Findings

Existence of nonlocal conserved currents.

Explicit form of initial supersymmetric charges.

Model remains integrable with free boundary conditions.

Abstract

We study classical integrability of the supersymmetric U(N) $\sigma$ model with the Wess-Zumino-Witten term on full and half plane. We demonstrate the existence of nonlocal conserved currents of the model and derive general recursion relations for the infinite number of the corresponding charges in a superfield framework. The explicit form of the first few supersymmetric charges are constructed. We show that the considered model is integrable on full plane as a concequence of the conservation of the supersymmetric charges. Also, we study the model on half plane with free boundary, and examine the conservation of the supersymmetric charges on half plane and find that they are conserved as a result of the equations of motion and the free boundary condition. As a result, the model on half plane with free boundary is integrable. Finally, we conclude the paper and some features and comments are presented.