Lie algebroid descriptions of T-duality
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2022-07-29
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The main idea of this work is to understand T-duality as a duality of geometric structures. In particular, we show that the structure of Lie algebroids in differential geometry is the one behind the description of T-duality. For instance, we give a geometric sense of it building a Lie bi-algebroid on the base manifold M of the bundles E and E coming from T-dual pairs (E, H) and (E, H). This description incorporates T-duality in a self-dual geometric concept. Thus we can understand T-duality as a compatibility condition of the Atiyah algebroids from the bundles E and E.