Higher-dimensional Chiral Algebras in the Jouanolou Model and free-field realization

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. One of our main results is the realization, using higher chiral operations, of the higher-dimensional Kac--Moody and Virasoro algebras.