Infinite dimensional topological-holomorphic symmetry in three dimensions
Abstract
We introduce a three-dimensional 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. Upon performing radial quantization, we construct the Fock space of the theory and, via a three-dimensional analog of the state-operator correspondence, we demonstrate that the algebra of local operators is endowed with the structure of a raviolo vertex algebra. 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.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Black Holes and Theoretical Physics
Topological Materials and Phenomena
Publication details
- Journal / source
- Physical review. D/Physical review. D.
- Publisher
- American Physical Society (APS)
- Volume
- 113
- Issue
- 12
- Publication date
- 30 April 2026
- Language
- EN