Realizing a higher derived current algebra of Kac-Moody type from a 3d Lax integrable field theory

Speaker: Hank Chen (BIMSA)

Time: 2026-01-17 14:00-16:00
Location: 1310, SIMIS

摘要：

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 (trivially) Lax integrable Wess-Zumino-Witten model, which realizes a raviolo version of the Kac-Moody current higher-algebra, semiclassically described as a centrally-extended infinite-dimensional differential graded Lie algebra. I will also describe how this theory can be quantized to an affine derived (raviolo) vertex algebra.