Black hole entropy and topological strings on generalized CY manifolds

Abstract

The H. Ooguri, A. Strominger and C. Vafa conjecture ZBH = |Ztop|2 is extended for the topological strings on generalized CY manifolds. It is argued that the classical black hole entropy is given by the generalized Hitchin functional, which defines by critical points a generalized complex structure on X. This geometry differs from an ordinary geometry if b1(X)≠0. In a critical point the generalized Hitchin functional equals to Legendre transform of the free energy of generalized topological string. The examples of T6 and T2 × K3 are considered in details. © SISSA 2006.