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

          @misc{ pirsa_PIRSA:25110057,
            doi = {10.48660/25110057},
            url = {https://pirsa.org/25110057},
            author = {},
            keywords = {Mathematical physics},
            language = {en},
            title = {Realizing a raviolo current higher-algebra of Kac-Moody type from a 3d topological-holomorphic field theory},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {nov},
            note = {PIRSA:25110057 see, \url{https://pirsa.org}}
          }
          

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.