# Classical and quantum stability in putative landscapes

## Abstract

Landscape analyses often assume the existence of large numbers of fields, N, with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N, eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N; scaling of couplings with N may also be necessary for perturbativity. We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. Finally, we consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.

- Authors:

- Univ. of California, Santa Cruz, CA (United States). Santa Cruz Inst. for Particle Physics and Dept. of Physics

- Publication Date:

- Research Org.:
- Univ. of California, Santa Cruz, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1360781

- Grant/Contract Number:
- SC0010107

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric Effective Theories; Supersymmetry Breaking

### Citation Formats

```
Dine, Michael.
```*Classical and quantum stability in putative landscapes*. United States: N. p., 2017.
Web. doi:10.1007/JHEP01(2017)082.

```
Dine, Michael.
```*Classical and quantum stability in putative landscapes*. United States. doi:10.1007/JHEP01(2017)082.

```
Dine, Michael. Wed .
"Classical and quantum stability in putative landscapes". United States.
doi:10.1007/JHEP01(2017)082. https://www.osti.gov/servlets/purl/1360781.
```

```
@article{osti_1360781,
```

title = {Classical and quantum stability in putative landscapes},

author = {Dine, Michael},

abstractNote = {Landscape analyses often assume the existence of large numbers of fields, N, with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N, eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N; scaling of couplings with N may also be necessary for perturbativity. We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. Finally, we consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.},

doi = {10.1007/JHEP01(2017)082},

journal = {Journal of High Energy Physics (Online)},

number = 1,

volume = 2017,

place = {United States},

year = {Wed Jan 18 00:00:00 EST 2017},

month = {Wed Jan 18 00:00:00 EST 2017}

}

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