Abstract
The description of 4D BPS black holes in terms of branes wrapped on various cycles in a Calabi–Yau space gives us the opportunity to study various issues in quantum gravity in a definite way by means of the worldvolume theory of the branes. In the particular example discussed here, there is a simple worldvolume description in terms of 2D Yang–Mills theory. The latter is an exactly solvable system of free fermions in one dimension. The exact answer for the free energy of this system can be written in a way that suggests an interpretation in terms of contributions from multiple (baby) universes.
Highlights
The study of quantum aspects of black holes has led to important progress in a deeper understanding of quantum gravity
At least in the case we study, the baby universes do not lead to a loss of quantum coherence, in accord with general arguments
One basic notion is that of black hole entropy, which was predicted by Bekenstein [1] and Hawking [2], through semiclassical reasoning, to be one quarter of the area of the horizon in Planck units
Summary
The study of quantum aspects of black holes has led to important progress in a deeper understanding of quantum gravity. In the context of certain extremal black holes obtained in compactifications of type II strings on Calabi-Yau three-folds these corrections are captured by topological string amplitudes [7] These results recently have led to a concrete formulation of the quantum corrected black hole entropy to all orders in string perturbation theory [8]. This states that the partition function of a statistical ensemble of black hole states ZBH is given by the norm-squared of the topological string wave function on the corresponding Calabi-Yau three-fold: 1550-7998= 2006=73(6)=066002(16)$23.00. V we interpret the nonperturbative large N corrections in the context of the holographically dual gravity solutions
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