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arXiv · 2603.12113

Integrability from Homotopy Algebras

Luigi Alfonsi·Leron Borsten·Mehran Jalali Farahani·Hyungrok Kim·Martin Wolf·Charles Alastair Stephen Young
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Abstract

Homotopy algebraic methods have become increasingly influential in studying field theories. We consider semi-holomorphic Chern-Simons theory and its relation with the principal chiral model. In particular, we establish an explicit quasi-isomorphism between the cyclic $L_\infty$-algebras governing both theories which directly gives the Lax connection. This provides a concrete example for studying integrability of a two-dimensional system through the homotopy algebraic lens.

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Luigi Alfonsi, Leron Borsten, Mehran Jalali Farahani, Hyungrok Kim, Martin Wolf, Charles Alastair Stephen Young. 2026-03-12. Integrability from Homotopy Algebras. https://arxiv.org/abs/2603.12113

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