Hartle-Hawking Wave-Function for Flux Compactifications

TL;DR

This paper interprets the topological string partition function as an exact wave-function of the universe in string theory, connecting it to black hole entropy and flux compactifications, with implications for holography and quantum corrections.

Contribution

It provides a novel interpretation of the topological string partition function as a wave-function in string theory, including all loop corrections and linking it to flux compactifications and holography.

Findings

Topological string partition function corresponds to a universe wave-function.

Black hole entropy relates to the square of the topological string wave-function.

Flux compactifications define a probability distribution on moduli space.

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.