Abstract
We study quantum entanglements of baby universes which appear in non-perturbative corrections to the OSV formula for the entropy of extremal black holes in type IIA string theory compactified on the local Calabi–Yau manifold defined as a rank 2 vector bundle over an arbitrary genus G Riemann surface. This generalizes the result for G = 1 in hep-th/0504221. Non-perturbative terms can be organized into a sum over contributions from baby universes, and the total wave-function is their coherent superposition in the third quantized Hilbert space. We find that half of the universes preserve one set of supercharges while the other half preserve a different set, making the total universe stable but non-BPS. The parent universe generates baby universes by brane/anti-brane pair creation, and baby universes are correlated by conservation of non-normalizable D-brane charges under the process. There are no other source of entanglement of baby universes, and all possible states are superposed with the equal weight.
Highlights
What distinguishes string theory from any other approaches to quantum gravity is, among others, the fact that one can estimate non-trivial quantum gravity effects in controlled approximations
The main ingredients of the OSV formula are topological string partition function Ztop of the Calabi-Yau manifold M and the partition function ZBH of black holes obtained by wrapping D-branes on cycles of M
As in the case of G = 1 studied in [11], the black hole partition function ZBH is expressed as a sum over Young diagrams with a fixed number of rows, and this structure naturally leads to the holomorphic factorization (1.2) in the limit when the number of rows is infinite
Summary
What distinguishes string theory from any other approaches to quantum gravity is, among others, the fact that one can estimate non-trivial quantum gravity effects in controlled approximations. The main ingredients of the OSV formula are topological string partition function Ztop of the Calabi-Yau manifold M and the partition function ZBH of black holes obtained by wrapping D-branes on cycles of M. One can identify the topological A-model string theory on M as the large N dual of the 2d Yang-Mills theory studied earlier in [10] In this case, non-perturbative corrections to (1.4) were evaluated in [11]. As in the case of G = 1 studied in [11], the black hole partition function ZBH is expressed as a sum over Young diagrams with a fixed number of rows, and this structure naturally leads to the holomorphic factorization (1.2) in the limit when the number of rows is infinite.
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