Topological T-Duality for Twisted Tori
Paolo Aschieri, Richard J. Szabo

TL;DR
This paper extends topological T-duality to a broad class of spaces including nilmanifolds and solvmanifolds, providing explicit constructions of T-duals as noncommutative tori and linking them to non-geometric string theory.
Contribution
It develops a general method for constructing T-duals using $C^*$-algebras, especially for almost abelian solvmanifolds, and characterizes when classical T-duals exist.
Findings
Explicit T-dual constructions for nilmanifolds and solvmanifolds.
Necessary and sufficient criteria for classical T-duals in group-theoretic terms.
Identification of T-duals as noncommutative tori with non-trivial Dixmier-Douady classes.
Abstract
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 . 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…
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