A bstractWe investigate degeneracies of BPS states of D-branes on compact Calabi-Yau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to… Expand

We give a physical explanation of the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum in Seiberg-Witten theories. In the process we give an exact description of the BPS instanton… Expand

We define chiral vertex operators and duality matrices and review the fundamental identities they satisfy. In order to understand the meaning of these equations, and therefore of conformal field… Expand

We consider a class of line operators in d = 4,N = 2 supersymmetric field theories which leave four supersymmetries unbroken. Such line operators support a new class of BPS states which we call… Expand

We discuss the relation between the Ramond-Ramond charges of D-branes and the topology of Chan-Paton vector bundles. We show that a topologically nontrivial normal bundle induces RR charge and that… Expand

We show that one can construct D-branes in parafermionic and WZW theories (and their orbifolds) which have very natural geometrical interpretations, and yet are not automatically included in the… Expand