BPS microstates and the open topological string wave function

Abstract

It has recently been conjectured that the closed topological string wave function computes a grand canonical partition function of Bogomol'nyi-Prasad-Sommerfield (BPS) black hole states in four dimensions: Z(BH) = vertical bar psi(top)vertical bar(2). We conjecture that the open topological string wave function also computes a grand canonical partition function, which sums over black holes bound to BPS excitations on D-branes wrapping cycles of the internal Calabi-Yau: Z(BPS)(open) = vertical bar psi(open)(top)vertical bar(2). This conjecture is verified in the case of Type IIA on a local Calabi-Yau three-fold involving a Riemann surface, where the degeneracies of BPS states can be computed in q-deformed two-dimensional Yang-Mills theory.