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In this paper, we initiate the study of C*-algebras endowed with a twisted action of a locally compact Abelian Lie group, and we construct a twisted crossed product, which is in general a nonassociative, noncommutative, algebra. The…

High Energy Physics - Theory · Physics 2014-11-18 Peter Bouwknegt , Keith Hannabuss , Varghese Mathai

We give a simplified definition of topological T-duality that applies to arbitrary torus bundles. The new definition does not involve Chern classes or spectral sequences, only gerbes and morphisms between them. All the familiar topological…

Differential Geometry · Mathematics 2015-05-08 David Baraglia

Let T be a torus. We show that Koszul duality can be used to compute the equivariant cohomology of topological T-spaces as well as the cohomology of pull backs of the universal T-bundle. The new features are that no further assumptions…

Algebraic Topology · Mathematics 2007-10-22 Matthias Franz

In this paper we study the topological T-dual of spaces with a non-free circle action mainly using the stack theory method of Bunke and co-workers \cite{Bunke1}. We first compare three formalisms for obtaining the Topological T-dual of a…

Mathematical Physics · Physics 2019-05-14 Ashwin S. Pande

We introduce a periodic form of the iterated algebraic K-theory of ku, the (connective) complex K-theory spectrum, as well as a natural twisting of this cohomology theory by higher gerbes. Furthermore, we prove a form of topological…

Algebraic Topology · Mathematics 2020-03-25 John A. Lind , Hisham Sati , Craig Westerland

We reconsider some older constructions of T-duality, based on automorphisms of the worldsheet operator algebra, in a modern context. It has been long known that at special points in the moduli space of torus compactifications, the target…

High Energy Physics - Theory · Physics 2021-05-19 Hasan Mahmood , R. A. Reid-Edwards

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…

High Energy Physics - Theory · Physics 2021-02-08 Paolo Aschieri , Richard J. Szabo

We explicitly construct the C*-algebras arising in the formalism of Topological T-duality due to Mathai and Rosenberg from string-theoretic data in several key examples. We construct a continuous-trace algebra with an action of ${\mathbb…

High Energy Physics - Theory · Physics 2008-10-30 Peter Bouwknegt , Ashwin S. Pande

The q-monopole bundle introduced previously is extended to a general construction for quantum group bundles with non-universal differential calculi. We show that the theory applies to several other classes of bundles as well, including…

q-alg · Mathematics 2008-02-03 Tomasz Brzezinski , Shahn Majid

We use the canonical description of T-duality as well as the formulation of T-duality in terms of chiral currents to investigate the geometric and non-geometric faces of closed string backgrounds originating from principal torus bundles…

High Energy Physics - Theory · Physics 2016-01-20 Ioannis Bakas , Dieter Lust

We introduce a new `Thom class' formulation of topological T-duality for principal torus bundles. This definition is equivalent to the established one of Bunke, Rumpf, and Schick but has the virtue of removing the global assumptions on the…

Geometric Topology · Mathematics 2024-07-08 Tom Dove , Thomas Schick

Spectral triples over noncommutative principal $\T^n$-bundles are studied, extending recent results about the noncommutative geometry of principal U(1)-bundles. We relate the noncommutative geometry of the total space of the bundle with the…

Quantum Algebra · Mathematics 2013-08-23 Alessandro Zucca , Ludwik Dabrowski

In this paper we study continuous bundles of C*-algebras which are non-commutative analogues of principal torus bundles. We show that all such bundles, although in general being very far away from being locally trivial bundles, are at least…

K-Theory and Homology · Mathematics 2014-02-26 Siegfried Echterhoff , Ryszard Nest , Herve Oyono-Oyono

We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the fibers. If the twist is associated with the…

Quantum Algebra · Mathematics 2017-06-27 Paolo Aschieri , Pierre Bieliavsky , Chiara Pagani , Alexander Schenkel

In this paper, we construct gauge bundles on a noncommutative toroidal orbifold $T^4_\theta/Z_2$. First, we explicitly construct a bundle with constant curvature connections on a noncommutative $T^4_\theta$ following Rieffel's method. Then,…

High Energy Physics - Theory · Physics 2009-10-31 Eunsang Kim , Hoil Kim , Chang-Yeong Lee

We show that the topological T-duality for circle bundles introduced in work of Bouwknegt-Evslin-Mathai can be interpreted as a form of Atiyah duality for twisted K-theory.

Algebraic Topology · Mathematics 2015-03-03 Craig Westerland

Topological T-duality is a relationship between pairs (E, P ) over a fixed space X, where E over X is a principal torus bundle and P over E is a twist, such as a gerbe of principal PU(H)-bundle. This is of interest to topologists because of…

K-Theory and Homology · Mathematics 2024-07-25 Tom Dove , Thomas Schick

We show that the supermembrane theory compactified on a torus is invariant under T-duality. There are two different topological sectors of the compactified supermembrane (M2) classified according to a vanishing or nonvanishing second…

High Energy Physics - Theory · Physics 2016-11-23 M. P. Garcia del Moral , J. M. Pena , A. Restuccia

We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically…

Differential Geometry · Mathematics 2023-05-26 Gil R. Cavalcanti , Marco Gualtieri

The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to…

High Energy Physics - Theory · Physics 2008-11-26 C. M. Hull