Overview
This research paper, titled "Nodal degeneration of chiral algebras I: Global structure and gluing formula," introduces a methodological framework for extending universal factorization algebras and demonstrates a specific property of their factorization homology. The study focuses on defining a natural extension for universal factorization algebra $\mathcal{A}$ to encompass families of stable punctured curves. Concurrently, it establishes a gluing formula for the resultant sheaf of factorization homology.
Approach
The methodology centers on integrating over all semistable modifications to achieve the extension of the universal factorization algebra $\mathcal{A}$. This integration process leads to the formation of a sheaf of factorization homology.
Findings
- A natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves has been defined. This extension is achieved by integrating over all semistable modifications.
- The resulting sheaf of factorization homology satisfies a natural gluing formula.
- This gluing formula is achieved by tensoring over a derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$. This mechanism generalizes the Verlinde formula, which is known for the gluing of conformal blocks.