Topological T-Duality for Twisted Tori
We apply the *-algebraic formalism of topological T-duality due to Mathai and Rosenberg to a broad class of topological spaces that include the torus bundles appearing in string theory compactifications with duality twists, such as nilmanifolds, as well as many other examples. We develop a simple pr...
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| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| ISSN: | 1815-0659 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211176 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Topological T-Duality for Twisted Tori. Paolo Aschieri and Richard J. Szabo. SIGMA 17 (2021), 012, 51 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862698701836779520 |
|---|---|
| author | Aschieri, Paolo Szabo, Richard J. |
| author_facet | Aschieri, Paolo Szabo, Richard J. |
| citation_txt | Topological T-Duality for Twisted Tori. Paolo Aschieri and Richard J. Szabo. SIGMA 17 (2021), 012, 51 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We apply the *-algebraic formalism of topological T-duality due to Mathai and Rosenberg to a broad class of topological spaces that include the torus bundles appearing in string theory compactifications with duality twists, such as nilmanifolds, as well as many other examples. We develop a simple procedure in this setting for constructing the T-duals starting from a commutative *-algebra with an action of ℝⁿ. We treat the general class of almost abelian solvmanifolds in arbitrary dimension in detail, where we provide necessary and sufficient criteria for the existence of classical T-duals in terms of purely group theoretic data, and compute them explicitly as continuous-trace algebras with non-trivial Dixmier-Douady classes. We prove that any such solvmanifold has a topological T-dual given by a *-algebra bundle of noncommutative tori, which we also compute explicitly. The monodromy of the original torus bundle becomes a Morita equivalence among the fiber algebras, so that these *-algebras rigorously describe the T-folds from non-geometric string theory.
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| first_indexed | 2026-03-18T10:20:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211176 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T10:20:00Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Aschieri, Paolo Szabo, Richard J. 2025-12-25T13:22:52Z 2021 Topological T-Duality for Twisted Tori. Paolo Aschieri and Richard J. Szabo. SIGMA 17 (2021), 012, 51 pages 1815-0659 2020 Mathematics Subject Classification: 46L55; 81T30; 16D90 arXiv:2006.10048 https://nasplib.isofts.kiev.ua/handle/123456789/211176 https://doi.org/10.3842/SIGMA.2021.012 We apply the *-algebraic formalism of topological T-duality due to Mathai and Rosenberg to a broad class of topological spaces that include the torus bundles appearing in string theory compactifications with duality twists, such as nilmanifolds, as well as many other examples. We develop a simple procedure in this setting for constructing the T-duals starting from a commutative *-algebra with an action of ℝⁿ. We treat the general class of almost abelian solvmanifolds in arbitrary dimension in detail, where we provide necessary and sufficient criteria for the existence of classical T-duals in terms of purely group theoretic data, and compute them explicitly as continuous-trace algebras with non-trivial Dixmier-Douady classes. We prove that any such solvmanifold has a topological T-dual given by a *-algebra bundle of noncommutative tori, which we also compute explicitly. The monodromy of the original torus bundle becomes a Morita equivalence among the fiber algebras, so that these *-algebras rigorously describe the T-folds from non-geometric string theory. We thank Ryszard Nest and Erik Plauschinn for helpful discussions. We thank the anonymous referees for their detailed suggestions. This research was supported by funds from Università del Piemonte Orientale (UPO). P.A. acknowledges partial support from INFN, CSN4, and Iniziativa Speci ca GSS. P.A. is affiliated with INdAM-GNFM. R.J.S. acknowledges a Visiting Professorship through UPO Internationalization Funds. R.J.S. also acknowledges the ArnoldRegge Centre for the visit and INFN. The work of R.J.S. was supported in part by the Consolidated Grant ST/P000363/1 from the UK Science and Technology Facilities Council. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Topological T-Duality for Twisted Tori Article published earlier |
| spellingShingle | Topological T-Duality for Twisted Tori Aschieri, Paolo Szabo, Richard J. |
| title | Topological T-Duality for Twisted Tori |
| title_full | Topological T-Duality for Twisted Tori |
| title_fullStr | Topological T-Duality for Twisted Tori |
| title_full_unstemmed | Topological T-Duality for Twisted Tori |
| title_short | Topological T-Duality for Twisted Tori |
| title_sort | topological t-duality for twisted tori |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211176 |
| work_keys_str_mv | AT aschieripaolo topologicaltdualityfortwistedtori AT szaborichardj topologicaltdualityfortwistedtori |