Black hole entropy and topological strings on generalized CY manifolds

The H. Ooguri, A. Strominger and C. Vafa conjecture $Z_{BH}=|Z_{top}|^2$ isextended for the topological strings on generalized CY manifolds. It is arguedthat the classical black hole entropy is given by the generalized Hitchinfunctional, which defines by critical points a generalized complex structure on$X$. This geometry differs from an ordinary geometry if $b_1(X)$ does notvanish. In a critical point the generalized Hitchin functional equals toLegendre transform of the free energy of generalized topological string. Theexamples of $T^6$ and $T^2 \times K3$ are considered in details.Comment: 19 pages; v2: references added, typos correcte