# 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.

- Authors:

- California Institute of Technology 452-48, Pasadena, California 91125 (United States)
- (United States)
- Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138 (United States)

- Publication Date:

- OSTI Identifier:
- 20782709

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.066010; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; COMPACTIFICATION; ENTROPY; QUANTUM FIELD THEORY; SPACE; STABILITY; STRING MODELS; WAVE FUNCTIONS

### Citation Formats

```
Gukov, Sergei, Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, Saraikin, Kirill, and Vafa, Cumrun.
```*Entropic principle and asymptotic freedom*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.066010.

```
Gukov, Sergei, Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, Saraikin, Kirill, & Vafa, Cumrun.
```*Entropic principle and asymptotic freedom*. United States. doi:10.1103/PHYSREVD.73.066010.

```
Gukov, Sergei, Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, Saraikin, Kirill, and Vafa, Cumrun. Wed .
"Entropic principle and asymptotic freedom". United States.
doi:10.1103/PHYSREVD.73.066010.
```

```
@article{osti_20782709,
```

title = {Entropic principle and asymptotic freedom},

author = {Gukov, Sergei and Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138 and Saraikin, Kirill and Vafa, Cumrun},

abstractNote = {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.},

doi = {10.1103/PHYSREVD.73.066010},

journal = {Physical Review. D, Particles Fields},

number = 6,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}

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