On algebraic structures in supersymmetric principal chiral model

TL;DR

This paper develops the algebraic canonical structure of the supersymmetric principal chiral model using Poisson current algebra, Lax matrices, and the r/s matrix formalism, revealing conserved quantities in involution.

Contribution

It introduces a new algebraic framework for the supersymmetric principal chiral model based on Poisson brackets and r/s matrix formalism, enhancing understanding of its integrability.

Findings

Derived the fundamental Poisson bracket of Lax matrices.

Computed the Poisson algebra of the monodromy matrix.

Identified conserved quantities in involution.

Abstract

Using the Poisson current algebra of the supersymmetric principal chiral model, we develop the algebraic canonical structure of the model by evaluating the fundamental Poisson bracket of the Lax matrices that fits into the rs matrix formalism of non-ultralocal integrable models. The fundamental Poisson bracket has been used to compute the Poisson bracket algebra of the monodromy matrix that gives the conserved quantities in involution.