TY - JOUR

T1 - Topological t-duality for twisted tori

AU - Aschieri, Paolo

AU - Szabo, Richard J.

N1 - Funding Information:
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 Specifica GSS. P.A. is affiliated to INdAM-GNFM. R.J.S. acknowledges a Visiting Professorship through UPO Internationalization Funds. R.J.S. also acknowledges the Arnold–Regge 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.
Publisher Copyright:
© 2021, Institute of Mathematics. All rights reserved.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021

Y1 - 2021

N2 - We apply the C∗-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 C∗-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 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 T-folds from non-geometric string theory.

AB - We apply the C∗-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 C∗-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 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 T-folds from non-geometric string theory.

KW - C-algebra bundles of noncommutative tori

KW - Mostow fibration of almost abelian solvmanifolds

KW - Noncommutative C-algebraic T-duality

KW - Nongeometric backgrounds

UR - http://www.scopus.com/inward/record.url?scp=85101128710&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2021.012

DO - 10.3842/SIGMA.2021.012

M3 - Article

AN - SCOPUS:85101128710

VL - 17

JO - Symmetry, Integrability and Geometry: Methods and Applications

JF - Symmetry, Integrability and Geometry: Methods and Applications

SN - 1815-0659

M1 - 012

ER -