Integrable Lambda Models And Chern-Simons Theories

Abstract

In this note we reveal a connection between the phase space of lambda models on $S^1\times \mathbb{R}$ and the phase space of double Chern-Simons theories on $D\times \mathbb{R}$ and explain in the process the origin of the non-ultralocality of the Maillet bracket, which emerges as a boundary algebra. In particular, this means that the (classical) $Ad{S}_5\times S^5$ lambda model can be understood as a double Chern-Simons theory defined on the Lie superalgebra $\mathfrak{psu}(2,2|4)$ after a proper dependence of the spectral parameter is introduced. This offers a possibility for avoiding the use of the problematic non-ultralocal Poisson algebras that preclude the introduction of lattice regularizations and the application of the QISM to string sigma models. The utility of the equivalence at the quantum level is, however, still to be explored.

27 pages. Published version

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Cited by in corpus (16)

• A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory
• Assembling integrable sigma-models as affine Gaudin models
• Integrable coupled sigma-models
• The most general $\lambda$-deformation of CFTs and integrability
• Novel all loop actions of interacting CFTs: Construction, integrability and RG flows
• Integrable $\mathcal{E}$-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
• Integrable Lambda Models And Chern-Simons Theories
• Holomorphic Chern-Simons theory and lambda models: PCM case
• Holomorphic Chern-Simons theory and affine Gaudin models
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Lambda Models From Chern-Simons Theories
• Exact results from the geometry of couplings and the effective action
• Giant Magnons of String Theory in the Lambda Background
• Symmetric space $\lambda$-model exchange algebra from 4d holomorphic Chern-Simons theory
• $\lambda$-Deformation Of The $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models