Entropic principle and asymptotic freedom

Creators: Gukov, Sergei; Saraikin, Kirill; Vafa, Cumrun

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.

Additional Information

© 2006 The American Physical Society. (Received 20 January 2006; published 21 March 2006) We would like to thank R. Dijkgraaf, S. Katz, A. Klemm, M. Roček, T. Oliker and H. Ooguri for valuable discussions. We also thank B. Fiol for pointing out a sign error in the large complex structure limit example, that appeared in the first version of the paper. This research was supported in part by NSF Grant Nos. PHY-0244821 and DMS-0244464. K. S. and S. G. are also supported in part by RFBR grant 04-02-16880. We would like to thank the 2005 Simons Workshop on Mathematics and Physics for providing a stimulating environment where part of this work was done. S. G. would also like to thank the KITP at Santa Barbara for hospitality during the completion of this work. While at KITP, the research of S. G. was supported in part by the NSF under grant PHY99-07949.

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