Entropic principle and asymptotic freedom

2005/09/30 by Sergei Gukov, Kirill Saraikin, Cumrun Vafa
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole thermodynamics #Cosmology and Gravitation Theories #Entropy (arrow of time) #Mathematics #Moduli #Moduli space #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #hep-th

paper · pdf · doi:10.1103/physrevd.73.066010

published as Phys.Rev.D73:066010,2006 · 25 pages, 2 figures, harvmac, v.2: sign error in the large complex structure example corrected

arxiv created 2006/02/15 · openalex publication_date 2006/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 Bogomolnyi-Prasad-Sommerfield 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.

Citations

• Arithmetic and Attractors
• Split attractor flows and the spectrum of BPS D-branes on the quintic
• A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
• Black hole attractors and the topological string
• de Sitter vacua in string theory
• A note of Shimura's paper ?discontinuous groups and abelian varieties?
• Basic results in vacuum statistics

Cited by

• Arrow of time in string theory