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arXiv · 2601.19993

The homological algebra of 2d integrable field theories

Marco Benini·Alexander Schenkel·Benoit Vicedo
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Abstract

This article provides a detailed and rigorous study of $4d$ semi-holomorphic Chern-Simons theories and their associated $2d$ integrable field theories from the homological perspective of $L_\infty$-algebras. Through the use of homotopy transfer techniques, it is shown precisely how both the integrable field theory and its corresponding Lax connection emerge from the $4d$ theory, which results in a novel perspective on Lax connections in terms of $L_\infty$-morphisms.

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Marco Benini, Alexander Schenkel, Benoit Vicedo. 2026-01-27. The homological algebra of 2d integrable field theories. https://arxiv.org/abs/2601.19993

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