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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Mathematics Subject Classifications: 81T20, 83C47, 83E30
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Ooguri, H., Vafa, C. & Verlinde, E. Hartle–Hawking Wave-Function for Flux Compactifications: the Entropic Principle. Lett Math Phys 74, 311–342 (2005). https://doi.org/10.1007/s11005-005-0022-x
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DOI: https://doi.org/10.1007/s11005-005-0022-x