Generalized complex geometry and T-duality

Details Generalized complex geometry and T-duality Generalized complex geometry and T-duality

2011-06-09

arxiv.org/abs/1106.1747v1

A Celebration of the Mathematical Legacy of Raoul Bott (CRM Proceedings & Lecture Notes), American Mathematical Society, 2010,

Mathematics

Differential Geometry

23 pages

Scientific paper

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 distinct torus bundles, and prescribes a method for transporting geometrical structures between them. We describe how this relation may be understood as a Courant algebroid isomorphism between the spaces in question. This then allows us to transport Dirac structures, generalized Riemannian metrics, generalized complex and generalized Kahler structures, extending the "Buscher rules" well-known to physicists. Finally, we re-interpret T-duality as a Courant reduction, and explain that T-duality between generalized complex manifolds may be viewed as a generalized complex submanifold (D-brane) of the product, in a way that establishes a direct analogy with the Fourier-Mukai transform.

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