Black hole entropy and topological strings on generalized CY manifolds

TL;DR

The paper addresses extending the OSV black hole/topological string relation to generalized CY manifolds. It argues that the classical entropy is captured by the generalized Hitchin functional and is computed from a Legendre transform of the imaginary part of the generalized topological string prepotential, with the pure spinor formalism living in $SO(6,6)$. In manifolds with nonzero $b_1(X)$, such as $T^6$ and $T^2\times K3$, the generalized Hitchin functional governs tree-level entropy, yielding explicit formulas like $S_{BH}=\pi\sqrt{I_4(p,q)}$ for $T^6$ and $S_{BH}=\pi\sqrt{p^2 q^2-(p\cdot q)^2}$ for $T^2\times K3$; these results connect generalized complex geometry, topological $\mathcal{J}$-model, and attractor physics. The study provides a unified framework for black hole entropy beyond Calabi–Yau compactifications and points to future work on higher-genus corrections and non-CY backgrounds. Overall, the generalized Hitchin functional emerges as a natural extension of Hitchin’s framework, preserving the OSV structure in a broader geometric setting.

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.