Journal
ANNALS OF PHYSICS
Volume 322, Issue 5, Pages 1096-1142Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2006.07.013
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We study the computational complexity of the physical problem of finding vacua of string theory which agree with data, such as the cosmological constant, and show that such problems are typically NP hard. In particular, we prove that in the Bousso-Polchinski model, the problem is NP complete. We discuss the issues this raises and the possibility that, even if we were to find compelling evidence that some vacuum of string theory describes our universe, we might never be able to find that vacuum explicitly. In a companion paper, we apply this point of view to the question of how early cosmology might select a vacuum. (c) 2006 Elsevier Inc. All rights reserved.
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