On the resolution of categorical symmetries in (Non-) Unitary Rational CFTs
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908678775373824 |
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| author | Bhattacharyya, Arpan Ghosh, Saptaswa Pal, Sounak Santara, Jagannath |
| author_facet | Bhattacharyya, Arpan Ghosh, Saptaswa Pal, Sounak Santara, Jagannath |
| contents | We explore several aspects of the categorical symmetry-resolved entanglement entropy (SREE) in two-dimensional Rational Conformal Field Theories (RCFTs) and express it directly in terms of the modular data of the theory. Motivated by arXiv:2409.02806, we provide a general formula for SREE that applies to symmetric (weakly/strongly) and cloaking boundary conditions as well as for fusion rings with multiplicities without invoking any SymTFT construction, relying instead on a purely 2d RCFT analysis. We check the formula against several explicit examples. Additionally, we study symmetry resolution for both categorical and invertible symmetries in (non-)diagonal RCFTs and comment on the subtleties that arise in these cases. Finally, we extend our analysis to diagonal non-unitary RCFTs, focusing on theories with generalized Haagerup-Izumi modular data, and find full agreement with the given formula. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_16363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the resolution of categorical symmetries in (Non-) Unitary Rational CFTs Bhattacharyya, Arpan Ghosh, Saptaswa Pal, Sounak Santara, Jagannath High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Algebra Quantum Physics We explore several aspects of the categorical symmetry-resolved entanglement entropy (SREE) in two-dimensional Rational Conformal Field Theories (RCFTs) and express it directly in terms of the modular data of the theory. Motivated by arXiv:2409.02806, we provide a general formula for SREE that applies to symmetric (weakly/strongly) and cloaking boundary conditions as well as for fusion rings with multiplicities without invoking any SymTFT construction, relying instead on a purely 2d RCFT analysis. We check the formula against several explicit examples. Additionally, we study symmetry resolution for both categorical and invertible symmetries in (non-)diagonal RCFTs and comment on the subtleties that arise in these cases. Finally, we extend our analysis to diagonal non-unitary RCFTs, focusing on theories with generalized Haagerup-Izumi modular data, and find full agreement with the given formula. |
| title | On the resolution of categorical symmetries in (Non-) Unitary Rational CFTs |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Algebra Quantum Physics |
| url | https://arxiv.org/abs/2511.16363 |