arXiv subjects

Lewis T. Cole

Publications and source records attributed to Lewis T. Cole.

7 recordsLinked to original sources

arXiv2026

Higher-Dimensional Integrable Scattering

This paper describes classical soliton scattering in the 2+1d integrable chiral model, related to the Bogomolny monopole equation and self-dual Yang-Mills, as a case study for higher-dimensional integrable scattering. Extended line solitons exhibit nontrivial scattering with lump solitons and with other line solitons, and $N \to N$ interactions can be factorised into a series of $2 \to 2$ interactions. Scattering between parallel line solitons in 3d is related to lump soliton scattering in 2d, allowing for direct comparison with results in 1+1d integrable field theories.

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arXiv2025

Integrable models from 4d holomorphic BF theory

We show how to construct 2d field theories with holomorphic integrability from defect setups in 4d holomorphic BF. In a simple example setup, we explicitly construct the 2d theory and perform an initial classical analysis. Making use of the symmetries, we are able to write down an infinite family of solutions to the equations of motion. Comparing with more typical integrable systems, we explain how 2d holomorphic integrability sits between the standard notions of integrability in one and two dimensions. These 2d theories are designed as toy models for integrable theories in three and four dimensions, many of which can be understood as partially or totally holomorphic. We comment on the implications for higher-dimensional integrability and aspects of quantization in the concluding remarks.

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arXiv2024

On topological defects in Chern-Simons theory

We construct a new class of topological surface defects in Chern-Simons theory with non-compact, non-Abelian gauge groups. These defects are characterized by isotropic subalgebras defined by solutions of the modified classical Yang-Baxter equation, and their fusion realizes a semi-group structure with non-invertible elements. From a Hamiltonian perspective, we calculate this fusion using the composition of Lagrangian correspondences within the Weinstein symplectic category. Applications include boundary terms and conditions in $AdS_3$ gravity and higher-spin theories.

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arXiv2024

Integrable Deformations from Twistor Space

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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arXiv2024

Integrability in Gravity from Chern-Simons Theory

This paper presents a new perspective on integrability in theories of gravity. We show how the stationary, axisymmetric sector of General Relativity can be described by the boundary dynamics of a four-dimensional Chern-Simons theory. This approach shows promise for simplifying solution generating methods in both General Relativity and higher-dimensional supergravity theories. The four-dimensional Chern-Simons theory presented generalises those for flat space integrable models by introducing a space-time dependent branch cut in the spectral plane. We also make contact with twistor space approaches to integrability, showing how the branch cut defects of four-dimensional Chern-Simons theory arise from a discrete reduction of six-dimensional Chern-Simons theory.

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arXiv2024

Gauging The Diamond: Integrable Coset Models from Twistor Space

Recent work has shown that certain integrable and conformal field theories in two dimensions can be given a higher-dimensional origin from holomorphic Chern-Simons in six dimensions. Along with anti-self-dual Yang-Mills and four-dimensional Chern-Simons, this gives rise to a diamond correspondence of theories. In this work we extend this framework to incorporate models realised through gaugings. As well as describing a higher-dimensional origin of coset CFTs, by choosing the details of the reduction from higher dimensions, we obtain rich classes of two-dimensional integrable models including homogeneous sine-Gordon models and generalisations that are new to the literature.

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arXiv2023

Unifying Approaches to Chiral Bosons

Chiral bosons, or self-dual p-form fields, are ubiquitous in string theoretic contexts but are challenging to treat. Lagrangian constructions invariably introduce a complexity be it auxiliary fields or sacrificing Lorentz invariance. In this note we show how to pass between such different approaches to chiral bosons starting from a Chern Simons point of view to recover formulations of Pasti, Sorokin and Tonin and of Mkrtchyan. This leads to a novel generalisation of the latter to include non-Abelian chiral bosons in 2-dimensions, and generalisations to include twisted self-duality which are relevant in T-duality symmetric approaches to string theory. Our approach also shows how global affine symmetries of two- and higher-dimensional chiral bosons emerge from broken Chern-Simons gauge transformations on the boundary.

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