Higher-dimensional Chiral Algebras in the Jouanolou Model

TL;DR

This paper extends the concept of chiral algebras to higher dimensions using Jouanolou torsors to model configuration space cohomology, introducing new operadic structures and higher-dimensional residues inspired by Feynman integrals.

Contribution

It generalizes chiral algebras to higher dimensions and develops a new operadic framework using Jouanolou torsors and higher-dimensional residues.

Findings

Established a model for higher-dimensional chiral algebras

Connected Jouanolou torsors with configuration space cohomology

Introduced higher-dimensional residues inspired by Feynman graphs

Abstract

We appeal to the theory of Jouanolou torsors to model the coherent cohomology of configuration spaces of points in d-dimensional affine space. Using this model, we develop the operadic notion of chiral operations, thus generalizing the notion of chiral algebras of Beilinson and Drinfeld to higher dimensions. To produce examples, we use a higher-dimensional conceptualization of the residue which is inspired by Feynman graph integrals.