Symmetric space λ-model exchange algebra from 4d holomorphic Chern-Simons theory

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.

Automated summary

In this paper, the classical exchange algebra of a lambda deformed string sigma model in a symmetric space is derived within the Hamiltonian formalism directly from a 4d holomorphic Chern-Simons theory. The explicit forms of the extended Lax connection and R-matrix in the Maillet bracket of the lambda model are explained based on a symmetry principle. This approach, based on a gauge theory, may offer a mechanism for addressing the non-ultralocality typically found in integrable string theories propagating in coset spaces.