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 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.

Predicting the cosmological constant from the causal entropic principle

“…(Despite our appropriation of the term "entropic principle", for which we apologize to the authors, there is also little relation to Ref. [42]. ) We could have adopted only the first conjecture, and continued to estimate the number of observers by more explicit anthropic criteria.…”

stu Black Holes Unveiled

“…This is also due to the issue of the Attractor Mechanism [7]- [10], a general phenomenon which occurs in extremal BHs coupled to Maxwell and scalar fields, as it is the case in supersymmetric theories of gravity [11]- [74] (for further developments, see also e.g. [75]- [78]). …”

On some properties of the attractor equations

“…Let us now consider the relevance of the above results in relation to the entropic functional given by Gukov, Saraikin and Vafa (GSV) in Eq. (3.1) of [9]. It reads…”

“…Instead, in the real basis the Hessian is a 2n V × 2n V real symmetric matrix, which may be decomposed as follows: 9) or its inverse…”

“…Finally, in Sect. 5 we try to connect our results to the entropic functional recently introduced in [9] in connection with the conjectured relation between the black hole entropy and the topological string partition function [10].…”