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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Topological $\mathrm{T}$-Duality for Twisted Tori
Paolo Aschieriabc, Richard J. Szaboadecf a Arnold–Regge Centre, Via P. Giuria 1, 10125 Torino, Italy
b Istituto Nazionale di Fisica Nucleare, Torino, Via P. Giuria 1, 10125 Torino, Italy
c Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale, Viale T. Michel 11, 15121 Alessandria, Italy
d Department of Mathematics, Heriot-Watt University,
Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, UK
e Higgs Centre for Theoretical Physics, Edinburgh, UK
f Maxwell Institute for Mathematical Sciences, Edinburgh, UK
Аннотация:
We apply the $C^*$-algebraic formalism of topological $\mathrm{T}$-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 $\mathrm{T}$-duals starting from a commutative $C^*$-algebra with an action of ${\mathbb R}^n$. 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 $\mathrm{T}$-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 $\mathrm{T}$-dual given by a $C^*$-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 $C^*$-algebras rigorously describe the $\mathrm{T}$-folds from non-geometric string theory.
Ключевые слова:
noncommutative $C^*$-algebraic $\mathrm{T}$-duality, nongeometric backgrounds, Mostow fibration of almost abelian solvmanifolds, $C^*$-algebra bundles of noncommutative tori.
Поступила: 30 июня 2020 г.; в окончательном варианте 22 января 2021 г.; опубликована 5 февраля 2021 г.
Образец цитирования:
Paolo Aschieri, Richard J. Szabo, “Topological $\mathrm{T}$-Duality for Twisted Tori”, SIGMA, 17 (2021), 012, 51 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1695 https://www.mathnet.ru/rus/sigma/v17/p12
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