A 3d integrable field theory with 2-Kac-Moody algebra symmetry (Virtual)

          @misc{ scivideos_PIRSA:25010078,
            doi = {10.48660/25010078},
            url = {https://pirsa.org/25010078},
            author = {Chen, Hank},
            keywords = {Mathematical physics},
            language = {en},
            title = {A 3d integrable field theory with 2-Kac-Moody algebra symmetry (Virtual)},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {jan},
            note = {PIRSA:25010078 see, \url{https://scivideos.org/pirsa/25010078}}
          }
          

Abstract

This talk is based on my recent joint works arXiv:2405.18625, arXiv:2307.03831 with Joaquin Liniado and Florian Girelli.
Based on Lie 2-groups, I will introduce a 3d topological-holomorphic integrable field theory W, which can be understood as a higher-dimensional version of the Wess-Zumino-Witten model. By studying its higher currents and holonomies, it is revealed that W is related to both the raviolo VOAs of Garner- Williams --- a type of derived higher quantum algebra --- and the lasagna modules of Manolescu-Walker-Wedrich --- a type of 4d higher-skein invariant. I will then analyze the Noether charges of W, and prove that its symmetries are encoded by a derived version of the Kac-Moody algebra. If time allows, I will discuss how W enjoys a certain notion of "higher Lax integrability".