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  • Open Access

Infinite dimensional topological-holomorphic symmetry in three dimensions

Hank Chen*

Joaquin Liniado†

  • Instituto de Física La Plata, UNLP and CONICET, Diagonal 113 esquina 63, La Plata, Argentina and School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, EH9 3FD, United Kingdom

  • *Contact author: chunhaochen@bimsa.cn
  • †Contact author: jliniado@ed.ac.uk
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Phys. Rev. D 113, 126003 – Published 4 June, 2026

DOI: https://doi.org/10.1103/vbgw-4xbn

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.

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Phys. Rev. D 113, 126003– Published 4 June, 2026
  • Received 18 December 2025
  • Accepted 30 April 2026
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