PIRSA:25110058 Conference Mathematical physics

DOI10.48660/25110058

Conference/School: Holomorphic-topological field theories and representation theory

(2025). Infinite Dimensional Topological-Holomorphic Symmetry in Three Dimensions. Perimeter Institute. https://pirsa.org/25110058

Infinite Dimensional Topological-Holomorphic Symmetry in Three Dimensions. Perimeter Institute, Nov. 04, 2025, https://pirsa.org/25110058 

@misc{ pirsa_PIRSA:25110058,
  doi = {10.48660/25110058},
  url = {https://pirsa.org/25110058},
  author = {},
  keywords = {Mathematical physics},
  language = {en},
  title = {Infinite Dimensional Topological-Holomorphic Symmetry in Three Dimensions},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {nov},
  note = {PIRSA:25110058 see, \url{https://pirsa.org}}
}

Abstract

We introduce a three-dimensional topological-holomorphic quantum field theory with an infinite-dimensional symmetry, realized explicitly through a centrally extended affine graded Lie algebra. This symmetry is a direct three-dimensional generalization of the chiral symmetry in the Wess-Zumino-Witten model. Accordingly, this setup provides a framework for extending the methods of two-dimensional conformal field theory to three dimensions, and we expect it to lay the groundwork for exact methods in three-dimensional quantum field theory.

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