Modular theory and symmetry resolution in hyperfinite von Neumann algebras
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915531073781760 |
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| author | Di Giulio, Giuseppe Dorband, Moritz Erdmenger, Johanna Scheppach, Henri |
| author_facet | Di Giulio, Giuseppe Dorband, Moritz Erdmenger, Johanna Scheppach, Henri |
| contents | We study modular theory in hyperfinite von Neumann algebras, i.e. in those of type II or type III, from the viewpoint of a subregion charge sector decomposition. We address this symmetry resolution by considering infinite tensor products of finite-dimensional algebras with fixed subregion charge values. An important ingredient is the combination of these algebras using direct integrals. This allows us to obtain the symmetry-resolved modular operator, modular flow, and modular correlation functions for hyperfinite algebras. Our approach establishes a mathematical foundation for recent results on symmetry resolution and modular theory in conformal field theory. Our analysis applies both to charges defined on a continuous range, or on a discrete set. The latter is of interest for condensed matter theory. Moreover, within the AdS/CFT correspondence we expect our findings to be relevant as a new ingredient for bulk spacetime reconstruction, including information from different boundary charge sectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modular theory and symmetry resolution in hyperfinite von Neumann algebras Di Giulio, Giuseppe Dorband, Moritz Erdmenger, Johanna Scheppach, Henri High Energy Physics - Theory Statistical Mechanics Operator Algebras We study modular theory in hyperfinite von Neumann algebras, i.e. in those of type II or type III, from the viewpoint of a subregion charge sector decomposition. We address this symmetry resolution by considering infinite tensor products of finite-dimensional algebras with fixed subregion charge values. An important ingredient is the combination of these algebras using direct integrals. This allows us to obtain the symmetry-resolved modular operator, modular flow, and modular correlation functions for hyperfinite algebras. Our approach establishes a mathematical foundation for recent results on symmetry resolution and modular theory in conformal field theory. Our analysis applies both to charges defined on a continuous range, or on a discrete set. The latter is of interest for condensed matter theory. Moreover, within the AdS/CFT correspondence we expect our findings to be relevant as a new ingredient for bulk spacetime reconstruction, including information from different boundary charge sectors. |
| title | Modular theory and symmetry resolution in hyperfinite von Neumann algebras |
| topic | High Energy Physics - Theory Statistical Mechanics Operator Algebras |
| url | https://arxiv.org/abs/2510.02441 |