Probing Geometry with Stability Conditions
arXiv:0905.3137
Abstract
The notion that the geometry of spacetime is given by the moduli space of 0-branes is examined in four examples of Calabi-Yau threefolds. An important consideration when determining the moduli space of D-branes is the stability condition and this is key in our analysis. In the first two examples, the flop and the orbifold blowup, no surprises are found. Next, an exoflop is considered where the linear sigma model implies a CP1 external to the Calabi-Yau threefold is part of the geometry. The 0-brane probe sees no such external CP1 and furthermore exhibits a surprising discontinuity when following an extremal transition associated to the exoflop. Finally we consider a hybrid model of a Landau--Ginzburg fibration over a CP1. Using the technology of matrix factorizations we find a D-brane probe whose moduli space is this CP1 but it is not a 0-brane and is not stable at the large radius limit of the Calabi-Yau manifold.
36 pages, refs added
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