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Integrability from Homotopy Algebras

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

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.

Integrability from Homotopy Algebras

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 -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.
Paper Structure (26 sections, 61 equations)

This paper contains 26 sections, 61 equations.

Table of Contents

  1. Introduction and summary
  2. Background.
  3. Summary of results.
  4. Outlook and the relative $L_\infty$-algebra perspective.
  5. Principal chiral model from semi-holomorphic Chern--Simons theory
  6. Setting.
  7. On-shell configurations.
  8. Remark.
  9. L Infinity-structure
  10. Semi-holomorphic Chern--Simons theory
  11. (Anti-)field spaces.
  12. $L_\infty$-algebra $\frL^{\rm shCS}$.
  13. Cyclic structure.
  14. Batalin--Vilkovisky action.
  15. Principal chiral model
  16. ...and 11 more sections