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Quasi- Poisson structures, Courant algebroids and Bianchi identities for non-geometric fluxes

Wednesday 27th June 2012 - 16:30 to 16:45
INI Seminar Room 2
The notion of non-geometric flux was introduced in string theory to correctly describe the degrees of freedom in four-dimensional effective superpotentials of type II flux compactifications. Whereas the H-flux is simply the field strength of the NS-NS B-field and the f-flux can be interpreted as the structure constants of a non-holonomic basis of the tangent bundle, the physical and mathematical properties of the remaining Q- and R-fluxes are to a great extent unknown. In this talk, we will first use the notion of a (quasi-)Poisson structure to re-derive directly on the tangent bundle the commutation relations containing all four fluxes as structure constants. As a consequence, we get Bianchi-type identities for the fluxes by writing down the Jacobi-identities for the algebra. Using these Bianchi-identities and the theory of quasi Lie-algebroids, we are able to identify the associated Courant algebroid structure, which is essential for dealing with all fluxes being non-zero.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons