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PreprintCC BY 4.0arXiv

On general background of quantum non-invertible symmetry in 2D

  • Jin Chen
  • Qiang Jia
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Abstract

We study the dual quantum symmetry Rep(G) in the two-dimensional theory T̃Rep(G) obtained by gauging a non-abelian symmetry G of TG, where for Lie groups G the gauging is understood as flat gauging. We develop a general framework for computing partition functions of T̃Rep(G) in arbitrary non-invertible symmetry backgrounds, represented by topological defect networks of Rep(G), in terms of the partition functions of the original theory TG. We also derive the inverse transformation, expressing partition functions of TG in G backgrounds in terms of those of T̃Rep(G). We test the framework in several examples, including finite groups with multiplicity-free and higher-multiplicity fusion rules, and discuss a formal extension to compact Lie groups, focusing on Rep(SU(2)).

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Cite

BibTeXRIS
BibTeX
@misc{chen2026general,
  title = {{On general background of quantum non-invertible symmetry in 2D}},
  author = {Jin Chen and Qiang Jia},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09550},
  eprint = {2609.09550},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09550},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On general background of quantum non-invertible symmetry in 2D
AU  - Jin Chen
AU  - Qiang Jia
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.09550
UR  - https://arxiv.org/abs/2609.09550
AB  - We study the dual quantum symmetry Rep(G) in the two-dimensional theory T̃_Rep(G) obtained by gauging a non-abelian symmetry G of T_G, where for Lie groups G the gauging is understood as flat gauging. We develop a general framework for computing partition functions of T̃_Rep(G) in arbitrary non-invertible symmetry backgrounds, represented by topological defect networks of Rep(G), in terms of the partition functions of the original theory T_G. We also derive the inverse transformation, expressing partition functions of T_G in G backgrounds in terms of those of T̃_Rep(G). We test the framework in several examples, including finite groups with multiplicity-free and higher-multiplicity fusion rules, and discuss a formal extension to compact Lie groups, focusing on Rep(SU(2)).
ER  -