D-BRANES ON Calabi–Yau MANIFOLDS

Abstract

In this review we study BPS D-branes on Calabi-Yau threefolds.Such D-branes naturally divide into two sets called A-branes and B-branes which are most easily understood from topological field theory.The main aim of this paper is to provide a self-contained guide to the derived category approach to B-branes and the idea of Π-stability.We argue that this mathematical machinery is hard to avoid for a proper understanding of B-branes.A-branes and B-branes are related in a very complicated and interesting way which ties in with the "homological mirror symmetry" conjecture of Kontsevich.We motivate and exploit this form of mirror symmetry.The examples of the quintic 3-fold, flops and orbifolds are discussed at some length.In the latter case we describe the rôle of McKay quivers in the context of D-branes.

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