PIRSA:25010078 Scientific Series Mathematical physics

DOI10.48660/25010078

Series: Mathematical Physics

Chen, H. (2025). A 3d integrable field theory with 2-Kac-Moody algebra symmetry (Virtual). Perimeter Institute. https://pirsa.org/25010078

Chen, Hank. A 3d integrable field theory with 2-Kac-Moody algebra symmetry (Virtual). Perimeter Institute, Jan. 23, 2025, https://pirsa.org/25010078 

@misc{ pirsa_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},
  year = {2025},
  month = {jan},
  note = {PIRSA:25010078 see, \url{https://pirsa.org}}
}

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".

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