Symmetric space $\lambda$-model exchange algebra from 4d holomorphic Chern-Simons theory

TL;DR

This paper derives the classical exchange algebra of a lambda deformed string sigma model in symmetric spaces from a 4d holomorphic Chern-Simons theory, offering a gauge-theoretic approach to integrability.

Contribution

It presents a novel derivation of the lambda model's exchange algebra directly from a 4d gauge theory, connecting integrable structures to holomorphic Chern-Simons theory.

Findings

Explicit form of the extended Lax connection derived

R-matrix structure explained from symmetry principles

Potential mechanism for addressing non-ultralocality in string theories

Abstract

We derive, within the Hamiltonian formalism, the classical exchange algebra of a lambda deformed string sigma model in a symmetric space directly from a 4d holomorphic Chern-Simons theory. The explicit forms of the extended Lax connection and R-matrix entering the Maillet bracket of the lambda model are explained from a symmetry principle. This approach, based on a gauge theory, may provide a mechanism for taming the non-ultralocality that afflicts most of the integrable string theories propagating in coset spaces.