Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-12-15
JHEP0609:034,2006
Physics
High Energy Physics
High Energy Physics - Theory
19 pages; v2: references added, typos corrected
Scientific paper
10.1088/1126-6708/2006/09/034
The H. Ooguri, A. Strominger and C. Vafa conjecture $Z_{BH}=|Z_{top}|^2$ 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 $b_1(X)$ does not vanish. In a critical point the generalized Hitchin functional equals to Legendre transform of the free energy of generalized topological string. The examples of $T^6$ and $T^2 \times K3$ are considered in details.
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