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

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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10 pages, entry for the 2009 FQXI Essay Contest

Scientific paper

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.

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