Mathematics Colloquia and Seminars

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Description

Geometric Transitions, first described by Vafa, provide a powerful scenario to connect string and gauge theories. In essence, they describe a transition between a geometry with D-branes warpping a certain cycle inside a Calabi-Yau to a background without branes but fluxes on a different Calabi-Yau. This correspondence has been shown to produce the same topological string amplitudes before and after transition. The theory on the D-branes gives rise to N=1 Super-Yang-Mills in 4 dimensions. The fluxes after the transtition create a superpotential that agrees with the known Veneziano-Yankielowicz superpotential for N=1 SYM. We generalized Vafa's scenario to a family of non-Kaehler backgrounds that have additional global symmetry, i.e. the corresponding gauge theory has flavor. In the discussion of these backgrounds I will comment on mirror symmetry with fluxes and lifts of SU(3) structure manifolds to G2 structure manifolds in M-theory. The topological string analysis and computation of superpotentials still remain, but it seems that generalized complex geometries naturally occur in this context.