Tensor complex renormalization with generalized symmetry and topological bootstrap
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914173565272064 |
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| author | Bao, Dong-Yu Cheng, Gong Song, Hong-Hao Gu, Zheng-Cheng |
| author_facet | Bao, Dong-Yu Cheng, Gong Song, Hong-Hao Gu, Zheng-Cheng |
| contents | Recent progress in generalized symmetry and topological holography has shown that, in conformal field theory (CFT), topological data from one dimensional higher can play a key role in determining local dynamics. Based on this insight, a fixed-point (FP) tensor complex (TC) for CFT has recently been constructed. In this work, we develop a TC renormalization (TCR) algorithm adapted to this CFT-based structure, forming a renormalization-group (RG) framework with generalized symmetry. We show that the full FP tensor can emerge from the RG flow starting with only the three-point function of the primary fields. Remarkably, even when starting solely from topological data, the RG process can still reconstruct the full FP tensor--a method we call as topological bootstrap. This approach deepens the connection between the topological and dynamical aspects of CFT and suggests pathways toward a fully algebraic description of gapless quantum states, with potential extensions to higher dimensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_22647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor complex renormalization with generalized symmetry and topological bootstrap Bao, Dong-Yu Cheng, Gong Song, Hong-Hao Gu, Zheng-Cheng Strongly Correlated Electrons Mathematical Physics Recent progress in generalized symmetry and topological holography has shown that, in conformal field theory (CFT), topological data from one dimensional higher can play a key role in determining local dynamics. Based on this insight, a fixed-point (FP) tensor complex (TC) for CFT has recently been constructed. In this work, we develop a TC renormalization (TCR) algorithm adapted to this CFT-based structure, forming a renormalization-group (RG) framework with generalized symmetry. We show that the full FP tensor can emerge from the RG flow starting with only the three-point function of the primary fields. Remarkably, even when starting solely from topological data, the RG process can still reconstruct the full FP tensor--a method we call as topological bootstrap. This approach deepens the connection between the topological and dynamical aspects of CFT and suggests pathways toward a fully algebraic description of gapless quantum states, with potential extensions to higher dimensions. |
| title | Tensor complex renormalization with generalized symmetry and topological bootstrap |
| topic | Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2511.22647 |