2008/10/24 by Peter Bouwknegt, Bouwknegt, Peter, Ashwin S. Pande +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #hep-th #math-ph #math.MP #math.OA
paper · pdf · doi:10.48550/arxiv.0810.4374
18 pages, no figures, uses xypic, minor typos corrected
openalex publication_date 2008/10/24 · arxiv created 2008/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Rd unique up to exterior equivalence from the data of a smooth \mathbb Td-equivariant gerbe on a trivial bundle X = W × \mathbb Td. We argue that the `noncommutative T-duals' of Mathai and Rosenberg, should be identified with the nongeometric backgrounds well-known in string theory. We also argue that the crossed-product C*-algebra \mathcal A \rtimes_α|\KZd \mathbb Zd should be identified with the T-folds of Hull which geometrize these backgrounds. We identify the charge group of D-branes on T-fold backgrounds in the C*-algebraic formalism of Topological T-duality. We also study D-branes on T-fold backgrounds. We show that the K-theory bundles studied by Echterhoff, Nest and Oyono-Oyono give a natural description of these objects.