Turing's Landscape: decidability, computability and complexity in string theory

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Rej, Abhijnan
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I argue that questions of algorithmic decidability, computability and complexity should play a larger role in deciding the "ultimate" theoretical description of the Landscape of string vacua. More specifically, I examine the notion of the average rank of the (unification) gauge group in the Landscape, the explicit construction of Ricci-flat metrics on Calabi-Yau manifolds as well as the computability of fundamental periods to show that undecidability questions are far more pervasive than that described in the work of Denef and Douglas.
Comment: 10 pages, entry for the 2009 FQXI Essay Contest
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High Energy Physics - Theory, General Relativity and Quantum Cosmology, Mathematical Physics
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