Black hole entropy and topological strings on generalized CY manifolds

TL;DR

This paper extends the black hole entropy and topological string conjecture to generalized Calabi-Yau manifolds, linking classical entropy to a generalized Hitchin functional and exploring specific examples.

Contribution

It introduces a generalized Hitchin functional for black hole entropy on non-traditional geometries, expanding the conjecture to broader classes of manifolds.

Findings

Classical black hole entropy equals the Legendre transform of generalized topological string free energy.

Generalized Hitchin functional defines a generalized complex structure on the manifold.

Examples of T^6 and T^2 x K3 illustrate the theoretical framework.

Abstract

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.