Paul Aspinwall

Probing Geometry with D-Branes and Stability.



Abstract

The notion that the geometry of spacetime is given by the moduli space of 0-branes is examined in some 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. I will 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. If time permits I will also consider an exoflop 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.