Realizing a raviolo current higher-algebra of Kac-Moody type from a 3d topological-holomorphic field theory

Abstract

A classic result of Hartogs says that, in complex dimension $n > 1$, holomorphic function on a punctured $n$-disc can be analytically continued to a function on the unpunctured $n$-disc. This motivated the use of *derived* differential geometry in, for instance, Faonte-Hennion-Kapranov, as a way to recover the "missing" negative modes in higher-dimensional current algebras. Following this line of thinking, together with the recent surge of interest in 3d topological-holomorphic (TH) field theories, the TH foliated version of the "formal punctured disc" was studied by Garner-Williams in 2023; this is known as the *formal raviolo*. In this talk, I will introduce a 3d TH version of the Wess-Zumino-Witten model which realizes a raviolo version of the Kac-Moody current higher-algebra, described as a centrally-extended infinite-dimensional $L_\infty$-algebra. By carrying out a "sphere quantization" via $S^2$-residues, this theory can then be quantized to an affine raviolo vertex operator algebra.