We study several aspects of the classical (gs → 0) limit of string theory. The first of these examines localized tachyon condensation in type II string theory on spacetime non-supersymmetric orbifolds C3/ZN a,b,c . By applying topological field theory methods to the N = (2,2) supersymmetric world-sheet theory, we find that the IR limit of the RG flow associated with tachyon condensation has a non-trivial chiral ring associated to non-geometric discrete vacua. The second part is devoted to studying D-branes in Calabi-Yau manifolds. We present a general method, based on simple notions of classical field theory, for treating bulk symmetries in a field theory on a space with a boundary. We apply this method to the N = (2,2) bulk supersymmetric non-linear sigma model and identify boundary conditions that preserve N = 2 world-sheet supersymmetry. This allows us to classify the possible BPS branes in Calabi-Yau three-folds in the large radius limit. Finally, in the third part we use topological methods and mirror symmetry to show in an example that, in certain limits, the low energy limit of D-branes wrapping a collapsing del Pezzo surface in a Calabi-Yau three-fold is described by an N = 1 supersymmetric quiver gauge theory. We then study some simple aspects of the quiver gauge theory description, including anomaly cancellation and the relation between theta-stability and classical supersymmetric vacua.
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