Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
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| Format: | Preprint |
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2025
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| _version_ | 1866910114382872576 |
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| author | Fukusumi, Yoshiki Kawamoto, Taishi |
| author_facet | Fukusumi, Yoshiki Kawamoto, Taishi |
| contents | We study conformal field theories (CFTs) and their classifications from a modern perspective based on the abstract algebraic formalism of symmetries or conserved charges, known as symmetry topological field theories (SymTFTs). By studying the algebraic structure of the SymTFTs in detail, we found a natural generalization of the quantum dimensions associated with (pseudo-)Hermitian systems and (non)-unitary CFTs. These generalized data of SymTFTs provide classifications of massless and massive renormalization group flows, which will describe the quantum phase transitions of the corresponding pseudo-Hermitian systems. Moreover, our discussions straightforwardly enable one to relate a general class of coset constructions or level-rank dualities to domain wall problems between topological quantum field theories (or a series of corresponding quantum phase transitions related to the Higgs mechanism). Our work provides a systematic reduction and classification of algebraic data, symmetries, for pseudo-Hermitian systems based on ideas from established mathematical fields, linear algebra and ring theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls Fukusumi, Yoshiki Kawamoto, Taishi High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology Mathematical Physics Quantum Physics We study conformal field theories (CFTs) and their classifications from a modern perspective based on the abstract algebraic formalism of symmetries or conserved charges, known as symmetry topological field theories (SymTFTs). By studying the algebraic structure of the SymTFTs in detail, we found a natural generalization of the quantum dimensions associated with (pseudo-)Hermitian systems and (non)-unitary CFTs. These generalized data of SymTFTs provide classifications of massless and massive renormalization group flows, which will describe the quantum phase transitions of the corresponding pseudo-Hermitian systems. Moreover, our discussions straightforwardly enable one to relate a general class of coset constructions or level-rank dualities to domain wall problems between topological quantum field theories (or a series of corresponding quantum phase transitions related to the Higgs mechanism). Our work provides a systematic reduction and classification of algebraic data, symmetries, for pseudo-Hermitian systems based on ideas from established mathematical fields, linear algebra and ring theory. |
| title | Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2511.11059 |