Higher Kac-Moody algebras and symmetries of holomorphic field theories

Understand

We introduce a higher dimensional generalization of the affine Kac-Moody algebra using the language of factorization algebras.

• In particular, on any complex manifold there is a factorization algebra of "currents" associated to any Lie algebra.
• We classify local cocycles of these current algebras, and compare them to central extensions of higher affine algebras recently proposed by Faonte-Hennion-Kapranov.
• A central goal of this paper is to witness higher Kac-Moody algebras as symmetries of a class of holomorphic quantum field theories.