Integrable Deformations from Twistor Space

Abstract

Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons in 6 dimensions. We provide the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. Starting from 6d holomorphic Chern-Simons theory on twistor space with a particular meromorphic 3-form $\Omega$, we construct the defect theory to find a novel 4d integrable field theory, whose equations of motion can be recast as the 4d anti-self-dual Yang-Mills equations. Symmetry reducing, we find a multi-parameter 2d integrable model, which specialises to the $\lambda$-deformation at a certain point in parameter space. The same model is recovered by first symmetry reducing, to give 4d Chern-Simons with generalised boundary conditions, and then constructing the defect theory.

38 pages, 1 figure

References in corpus (27)

• On integrability of the Yang-Baxter $\si$-model
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Gauge Theory and Integrability, II
• Gauge Theory and Integrability, I
• Supersymmetric gauge theory and the Yangian
• A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory
• Integrable flows between exact CFTs
• Assembling integrable sigma-models as affine Gaudin models
• Gauge Theory And Integrability, III
• 4-dimensional Chern-Simons theory and integrable field theories
• Quantization of open-closed BCOV theory, I
• Double and cyclic $\lambda$-deformations and their canonical equivalents
• Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory
• Integrable sigma models and 2-loop RG flow
• Integrable $\mathcal{E}$-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
• Local charges in involution and hierarchies in integrable sigma-models
• Quantizing the non-linear graviton
• Integrable deformations of coupled sigma-models
• Twisted Holography
• Integrable degenerate $\mathcal{E}$-models from 4d Chern-Simons theory
• Deformed Integrable Models from Holomorphic Chern-Simons Theory
• Lax formulation for harmonic maps to a moduli of bundles
• Dualities and Discretizations of Integrable Quantum Field Theories from 4d Chern-Simons Theory

Cited by in corpus (5)

• Higher Gauge Theory and Integrability
• Gauging The Diamond: Integrable Coset Models from Twistor Space
• Integrability in Gravity from Chern-Simons Theory
• Integrability of the $\lambda$-deformation of the PCM with spectators
• Integrable models from 4d holomorphic BF theory