Abstract
Abstract We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes.
Highlights
Part of first order Poisson sigma characterized by a 2-form B and a bivector θ to a threedimensional WZW term
We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes
Let us note that the noncommutativity of D-branes can be seen as the noncommutativity of the string endpoints in the open topological Poisson sigma model [3], which fits naturally to their role in both the integration as well as deformation quantization of Poisson structures
Summary
We recall some basic facts regarding generalized geometry, see, e.g., [2, 26]. The corresponding fiberwise metric (·, ·)τ can be written in the block matrix form (V + ξ, W + η)τ =. In the case we will consider later, L will be given as a graph of a Poisson tensor θ and the corresponding foliation of M will be the foliation generated by Hamiltonian vector fields, i.e., by symplectic leaves of θ. In this case we will identify the symplectic leaves and D-branes
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