TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.1.008
TI  - Integrable deformations from twistor space
PY  - 2024/07/10
UR  - https://www.scipost.org/SciPostPhys.17.1.008
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 1
SP  - 008
A1  - Cole, Lewis T.
AU  - Cullinan, Ryan A.
AU  - Hoare, Ben
AU  - Liniado, Joaquin
AU  - Thompson, Daniel C.
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.17.1.008,
	title={{Integrable deformations from twistor space}},
	author={Lewis T. Cole and Ryan A. Cullinan and Ben Hoare and Joaquin Liniado and Daniel C. Thompson},
	journal={SciPost Phys.},
	volume={17},
	pages={008},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.1.008},
	url={https://scipost.org/10.21468/SciPostPhys.17.1.008},
}