Categorical continuous symmetry
5 affiliations
- 1Korea Advanced Institute of Science Technology
- 2Peking University
- 3Perimeter Institute for Theoretical Physics
- 4East China Normal University
- 5The University of Tokyo
Abstract
A bstract We define the symmetry category in 1+1d for continuous 0-form G -symmetry to be Sky τ ( G ), the category of skyscraper sheaves of finite dimensional vector spaces with finite support on the group manifold of G , where τ ∈ H 4 ( BG, ℤ) is the anomaly. We propose that the corresponding 2+1d SymTFT is described by the Drinfeld center of Sky τ ( G ). We show explicitly the way that τ twists the convolution tensor product of the objects of Sky τ ( G ). As a concrete example, we present the S and T -matrices for the simple anyons of the resulting Z ( Sky τ ( G )) category for G = U (1), both for the cases without or with anomaly, and discuss the topological boundary conditions as Lagrangian algebra of Z ( Sky τ ( U (1))). We also present the definition of Sky τ ( G ) and Z ( Sky τ ( G )) for the non-abelian case of G = SU (2), as well as the speculated modular data. We point out that in order to have a physically relevant center and Lagrangian algebras, it is necessary to generalize Sky τ ( G ) to a larger category, which we argue to be closely related to the category of quasi-coherent sheaves on G ℂ with convolution tensor product twisted by τ .
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BibTeX
@article{jia2026categorical,
title = {{Categorical continuous symmetry}},
author = {Qiang Jia and Ran Luo and Jiahua Tian and Yi-Nan Wang and Yi Zhang A},
journal = {Journal of High Energy Physics},
year = {2026},
month = jun,
doi = {10.1007/jhep06(2026)031},
url = {https://doi.org/10.1007/jhep06(2026)031},
note = {CC BY},
}
RIS
TY - JOUR
TI - Categorical continuous symmetry
AU - Qiang Jia
AU - Ran Luo
AU - Jiahua Tian
AU - Yi-Nan Wang
AU - Yi Zhang A
PY - 2026
DA - 2026/06/03
JO - Journal of High Energy Physics
DO - 10.1007/jhep06(2026)031
UR - https://doi.org/10.1007/jhep06(2026)031
AB - A bstract We define the symmetry category in 1+1d for continuous 0-form G -symmetry to be Sky τ ( G ), the category of skyscraper sheaves of finite dimensional vector spaces with finite support on the group manifold of G , where τ ∈ H 4 ( BG, ℤ) is the anomaly. We propose that the corresponding 2+1d SymTFT is described by the Drinfeld center of Sky τ ( G ). We show explicitly the way that τ twists the convolution tensor product of the objects of Sky τ ( G ). As a concrete example, we present the S and T -matrices for the simple anyons of the resulting Z ( Sky τ ( G )) category for G = U (1), both for the cases without or with anomaly, and discuss the topological boundary conditions as Lagrangian algebra of Z ( Sky τ ( U (1))). We also present the definition of Sky τ ( G ) and Z ( Sky τ ( G )) for the non-abelian case of G = SU (2), as well as the speculated modular data. We point out that in order to have a physically relevant center and Lagrangian algebras, it is necessary to generalize Sky τ ( G ) to a larger category, which we argue to be closely related to the category of quasi-coherent sheaves on G ℂ with convolution tensor product twisted by τ .
SN - 1029-8479
SN - 1126-6708
SN - 1127-2236
ER -