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Split states, entropy enigmas, holes and halos
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
Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
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
Classical and quantum conformal field theory
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
Framed BPS states
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
K-theory and Ramond-Ramond charge
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
Geometrical interpretation of D-branes in gauged WZW models
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