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Hamiltonian perspective on generalized complex structure. (English) Zbl 1104.53077
Author’s summary: In this note we clarify the relation between extended world-sheet super-symmetry and generalized complex structure. The analysis is based on the phase space description of a wide class of sigma models. We point out the natural isomorphism between the group of orthogonal automorphisms of the Courant bracket and the group of local canonical transformations of the cotangent bundle of the loop space. Indeed this fact explains the natural relation between the world-sheet and the geometry of $$T \oplus T^*$$. We discuss D-branes in this perspective.

MSC:
 53C80 Applications of global differential geometry to the sciences 53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry 81T60 Supersymmetric field theories in quantum mechanics
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