Homotopy chiral algebras

TL;DR

This paper introduces homotopy chiral algebras as a higher homotopy generalization of chiral algebras and demonstrates that the Cech complex of a sheaf of chiral algebras naturally admits such a structure.

Contribution

It defines homotopy chiral algebras and proves the Cech complex of a sheaf of chiral algebras has this structure, extending the theory of chiral algebras.

Findings

Homotopy chiral algebras generalize traditional chiral algebras.

The Cech complex of a sheaf of chiral algebras admits a homotopy chiral algebra structure.

Provides a new framework for understanding chiral algebra sheaves.

Abstract

We define a notion of a homotopy chiral algebra (HCA), which means a chiral algebra up to higher homotopies, and prove that the Cech complex of a sheaf of chiral algebras admits a structure of a HCA.