Integrability from Homotopy Algebras

TL;DR

This paper demonstrates how homotopy algebraic methods can be used to establish integrability in two-dimensional field theories by explicitly relating the algebraic structures of Chern-Simons theory and the principal chiral model.

Contribution

It constructs an explicit quasi-isomorphism between cyclic L-infinity algebras of two theories, linking homotopy algebra to integrability.

Findings

Explicit Lax connection derived from algebraic isomorphism

Homotopy algebra provides a new perspective on integrability

Bridges between field theories via algebraic structures

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.