From topological-holomorphic Chern-Simons to integrable field theories via homotopy transfer
| When |
Oct 13, 2026
from 01:30 to 02:30 |
|---|---|
| Where | Amphithéâtre E |
| Contact Name | Marc Magro |
| Attendees |
Benoit Vicedo |
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Mardi 13 octobre 2026
Title: From topological-holomorphic Chern-Simons to integrable field theories via homotopy transfer
Benoit Vicedo (University of York, United Kingdom)
Abstract: In the modern gauge-theoretic approach to integrable field theory of Costello and Yamazaki, many integrable field theories (IFTs) on a 2-dimensional spacetime \Sigma can be obtained from 4-dimensional semi-holomorphic Chern-Simons theory on \Sigma \times \mathbb{C}P^1 with suitable singular structures and boundary conditions imposed on the fields. In particular, the spectral parameter of the IFT acquires a geometric interpretation as a coordinate on the \mathbb{C}P^1 factor. I will describe a homotopy-algebraic formulation of this construction in which classical field theories are encoded by cyclic L_\infty-algebras. In this framework, ``integrating out'' the spectral \mathbb{C}P^1 is realised by homotopy transfer to its partial Dolbeault cohomology. The resulting transferred L_\infty-algebra describes the 2d IFT, while its Lax connection arises naturally from an L_\infty-morphism to an algebra encoding meromorphic flat connections. I will then explain how this perspective naturally generalises the Costello-Yamazaki framework to higher dimensions, leading to topological-holomorphic higher Chern-Simons theories and a corresponding notion of higher Lax connection. The talk will be based on the joint work with M. Benini, R. Cullinan and A. Schenkel [2601.19993, 2604.24864, 2607.12142], as well as work in progress.