Nodal degeneration of chiral algebras

TL;DR

This paper introduces a sheaf of factorization algebras over stable curves, providing a gluing formula for chiral homology that generalizes vertex algebra sheaves and Verlinde formulas.

Contribution

It defines a new sheaf of factorization algebras for stable curves and proves a gluing formula for chiral homology, extending existing theories.

Findings

Established a sheaf of factorization algebras over stable curves.

Proved a gluing formula for the associated sheaf of chiral homology.

Generalized the Verlinde formula for conformal blocks.

Abstract

Given a family of stable curves, we define a sheaf of factorization algebras associated to any universal factorization algebra, and prove a gluing formula for the corresponding sheaf of chiral homology, generalizing the sheaves of vertex algebras and the associated Verlinde formula for gluing of conformal blocks.