Generalized complex geometry and T-duality
By G. Cavalcanti, M. Gualtieri. 2011
150 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/607b451aabd346a423fb10da2954e1d5fd494e6b
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Citations in the corpus
- Duality Symmetric String and M-Theory (2013, background): “ymmetry [130, 67]; brane wrapping rules [166, 167, 168] and the E11 [169] derivation of double field theory [170, 171] (of which we shall return to later); investigation of the relevant Lie algebroids [172, 173, 174, 175]. 15This list is not intended to be exhaustive but we hope it serves as a useful”