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Hartle-Hawking Wave-Function for Flux Compactifications

Hirosi Ooguri·Cumrun Vafa·Erik Verlinde
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Abstract

We argue that the topological string partition function, which has been known to correspond to a wave-function, can be interpreted as an exact ``wave-function of the universe'' in the mini-superspace sector of physical superstring theory. This realizes the idea of Hartle and Hawking in the context of string theory, including all loop quantum corrections. The mini-superspace approximation is justified as an exact description of BPS quantities. Moreover this proposal leads to a conceptual explanation of the recent observation that the black hole entropy is the square of the topological string wave-function. This wave-function can be interpreted in the context of flux compactification of all spatial dimensions as providing a physical probability distribution on the moduli space of string compactification. Euclidean time is realized holographically in this setup.

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Hirosi Ooguri, Cumrun Vafa, Erik Verlinde. 2005-05-10. Hartle-Hawking Wave-Function for Flux Compactifications. https://doi.org/10.1007/s11005-005-0022-x

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