The Entropic Principle and Asymptotic Freedom

Abstract

Motivated by the recent developments about the Hartle-Hawking wave function associated to black holes, we formulate an entropy functional on the moduli space of Calabi-Yau compactifications. We find that the maximization of the entropy is correlated with the appearance of asymptotic freedom in the effective field theory. The points where the entropy is maximized correspond to points on the moduli which are maximal intersection points of walls of marginal stability for BPS states. We also find an intriguing link between extremizing the entropy functional and the points on the moduli space of Calabi-Yau three-folds which admit a `quantum deformed' complex multiplication.

25 pages, 2 figures, harvmac, v.2: sign error in the large complex structure example corrected

References in corpus (4)

• Black Hole Attractors and the Topological String
• Hartle-Hawking Wave-Function for Flux Compactifications
• Basic results in Vacuum Statistics
• A Stringy Wave Function for an S^3 Cosmology

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