Hartle–Hawking Wave-Function for Flux Compactifications: the Entropic Principle

By Hirosi Ooguri, C. Vafa, Erik P. Verlinde. 2005

160 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/453569c208670a1a0d7f6025ecac4217659a69a0

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Citations in the corpus

Black hole partition functions and duality (2006, background): “Interesting progress in this direction can be found in [14, 15, 16 ].”
Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions (2006, background): “the properties of 4d black holes [10] and the wave function in mini superspace [ 11 ].”
Holographic description of AdS cosmologies (2005, background): “(16)Possible connections between the Hartle-Hawking wave function and string theory were also discussed in [36] and [37].”
ABJM theory as a Fermi gas (2011, background): “It is interesting to point out that the universal role of the Airy function in summing up 1/N corrections was already proposed in [16], in the different but related context of five-dimensional black holes made out of M2 branes in certain Calabi–Yau compactifications1.”
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant (2012, background): “9) The appearance of the Airy function [33] is also encountered in the context of M-theory flux compactification [46].”
Type IIA Moduli Stabilization (2005, methodology): “Finally, it would be interesting to see if there is a direct relation between our IIA constructions and some topological field theory construction, which could provide an analogue of the Hartle-Hawking wavefunction [43] for these vacua – such a construction has been obtained for some simple classes ”
Summing up all genus free energy of ABJM matrix model (2011, methodology): “Meanwhile, in a somewhat different context of M-theory flux compactification, it was argued that the norm square of the “wave-function of the universe” or the 5d black hole entropy was given by the Airy function [ 53 ].”
Instanton effects in ABJM theory from Fermi gas approach (2012, methodology): “The Airy function has the integral representation of the exponentiated cubic term, which looks similar to the partition function of the Chern-Simons theory, and appears also in other contexts of M-theory [12].”
Split states, entropy enigmas, holes and halos (2007, background): “Of course, this observation has been made before [113, 114], but there have been some difficulties making this proposal precise.”
Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory (2008, result): “1 This picture has been advocated by Cumrun Vafa, and is also close to the ideas in [ 22 ].”