2025/06/11 by Felder, Laura O., Gui, Zhengping, Young, Charles A. S. · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2506.09728
Vertex algebras are equivalent to translation-equivariant chiral algebras on \mathbbA1, in the sense of Beilinson and Drinfeld. In this paper we give an algebraic construction of a chiral algebra on \mathbbAn; this can be seen as an algebraic construction of a higher-dimensional vertex algebra. We introduce a model, in dg commutative algebras, of the derived algebra of functions on the configuration space of k distinct labelled marked points in \mathbbAn. Working in this model -- which we call the polysimplicial model -- we obtain a dg operad of chiral operations on a degree-shifted copy of the canonical sheaf. We prove that there is a quasi-isomorphism, to this dg operad, from the Lie-infinity operad. This result makes the shifted canonical sheaf into a first example of a homotopy polysimplicial chiral algebra on \mathbbAn, in a sense which generalizes to higher dimensions Malikov and Schechtman's notion of a homotopy chiral algebra.