A type I approximation of the crossed product
Abstract I show that an analog of the crossed product construction that takes type 𝐼𝐼𝐼1 algebras to type 𝐼𝐼 algebras exists also in the type 𝐼 case. This is particularly natural when the local algebra is a non-trivial direct sum of type 𝐼 factors. Concretely, I rewrite the usual type 𝐼 trace in a di...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2024)123 |
| _version_ | 1797341363048546304 |
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| author | Ronak M. Soni |
| author_facet | Ronak M. Soni |
| author_sort | Ronak M. Soni |
| collection | DOAJ |
| description | Abstract I show that an analog of the crossed product construction that takes type 𝐼𝐼𝐼1 algebras to type 𝐼𝐼 algebras exists also in the type 𝐼 case. This is particularly natural when the local algebra is a non-trivial direct sum of type 𝐼 factors. Concretely, I rewrite the usual type 𝐼 trace in a different way and renormalise it. This new renormalised trace stays well-defined even when each factor is taken to be type 𝐼𝐼𝐼. I am able to recover both type 𝐼𝐼 ∞ as well as type 𝐼𝐼1 algebras by imposing different constraints on the central operator in the code. An example of this structure appears in holographic quantum error-correcting codes; the central operator is then the area operator. |
| first_indexed | 2024-03-08T10:16:56Z |
| format | Article |
| id | doaj.art-a0c78431a22b4bfcb53faec82bff9785 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T10:16:56Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a0c78431a22b4bfcb53faec82bff97852024-01-28T12:25:10ZengSpringerOpenJournal of High Energy Physics1029-84792024-01-012024111910.1007/JHEP01(2024)123A type I approximation of the crossed productRonak M. Soni0Department of Applied Mathematics and Theoretical Physics, University of CambridgeAbstract I show that an analog of the crossed product construction that takes type 𝐼𝐼𝐼1 algebras to type 𝐼𝐼 algebras exists also in the type 𝐼 case. This is particularly natural when the local algebra is a non-trivial direct sum of type 𝐼 factors. Concretely, I rewrite the usual type 𝐼 trace in a different way and renormalise it. This new renormalised trace stays well-defined even when each factor is taken to be type 𝐼𝐼𝐼. I am able to recover both type 𝐼𝐼 ∞ as well as type 𝐼𝐼1 algebras by imposing different constraints on the central operator in the code. An example of this structure appears in holographic quantum error-correcting codes; the central operator is then the area operator.https://doi.org/10.1007/JHEP01(2024)1231/𝑁 ExpansionAdS-CFT CorrespondenceGauge-Gravity Correspondence |
| spellingShingle | Ronak M. Soni A type I approximation of the crossed product Journal of High Energy Physics 1/𝑁 Expansion AdS-CFT Correspondence Gauge-Gravity Correspondence |
| title | A type I approximation of the crossed product |
| title_full | A type I approximation of the crossed product |
| title_fullStr | A type I approximation of the crossed product |
| title_full_unstemmed | A type I approximation of the crossed product |
| title_short | A type I approximation of the crossed product |
| title_sort | type i approximation of the crossed product |
| topic | 1/𝑁 Expansion AdS-CFT Correspondence Gauge-Gravity Correspondence |
| url | https://doi.org/10.1007/JHEP01(2024)123 |
| work_keys_str_mv | AT ronakmsoni atypeiapproximationofthecrossedproduct AT ronakmsoni typeiapproximationofthecrossedproduct |