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

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.

arXiv commentPublished version

References in corpus (22)

• An integrable deformation of the AdS_5 x S^5 superstring action
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Three-dimensional quantum geometry and black holes
• Global Charges in Chern-Simons theory and the 2+1 black hole
• An Integrable Deformation of the AdS5 x S5 Superstring
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Integrable Deformations of Strings on Symmetric Spaces
• Gauge Theory and Integrability, II
• Gauge Theory and Integrability, I
• Supersymmetric gauge theory and the Yangian
• A short review on Noether's theorems, gauge symmetries and boundary terms
• A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Gauge Theory And Integrability, III
• The Chern-Simons Origin of Superstring Integrability
• S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models
• Integrable Lambda Models And Chern-Simons Theories
• Holomorphic Chern-Simons theory and lambda models: PCM case
• Lambda Models From Chern-Simons Theories

Cited by in corpus (3)

• 4-dimensional Chern-Simons theory and integrable field theories
• Integrable degenerate $\mathcal{E}$-models from 4d Chern-Simons theory
• 3-dimensional mixed BF theory and Hitchin's integrable system