Higher Kac–Moody algebras and symmetries of holomorphic field theories

We introduce a higher dimensional generalization of the affine Kac-Moody algebra using language factorization algebras. In particular, on any complex manifold there is currents associated to Lie algebra. classify local cocycles these current algebras, and compare them central extensions algebras recently proposed by Faonte-Hennion-Kapranov. A goal this paper witness as symmetries class holomorphic quantum field theories. we prove free realization an also develop theory q-characters for in terms homology. Finally, exhibit large N behavior their relationship non-commutative