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arXiv · 2311.17551

Integrable Deformations from Twistor Space

Lewis T. Cole·Ryan A. Cullinan·Ben Hoare·Joaquin Liniado·Daniel C. Thompson
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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 $Ω$, 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 $λ$-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.

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Lewis T. Cole, Ryan A. Cullinan, Ben Hoare, Joaquin Liniado, Daniel C. Thompson. 2024-10-30. Integrable Deformations from Twistor Space. https://doi.org/10.21468/scipostphys.17.1.008

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