### Abstract

Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and nonsupersymmetric string vacua fills out a landscape whose features are largely unknown. It is then hoped that progress in extracting phenomenological predictions from string theory-such as correlations between gauge groups, matter representations, potential values of the cosmological constant, and so forth-can be achieved through statistical studies of these vacua. To date, most of the efforts in these directions have focused on type I vacua. In this note, we present the first results of a statistical study of the heterotic landscape, focusing on more than 105 explicit nonsupersymmetric tachyon-free heterotic string vacua and their associated gauge groups and one-loop cosmological constants. Although this study has several important limitations, we find a number of intriguing features which may be relevant for the heterotic landscape as a whole. These features include different probabilities and correlations for different possible gauge groups as functions of the number of orbifold twists. We also find a vast degeneracy amongst nonsupersymmetric string models, leading to a severe reduction in the number of realizable values of the cosmological constant as compared with naïve expectations. Finally, we find strong correlations between cosmological constants and gauge groups which suggest that heterotic string models with extremely small cosmological constants are overwhelmingly more likely to exhibit the standard model gauge group at the string scale than any of its grand-unified extensions. In all cases, heterotic world sheet symmetries such as modular invariance provide important constraints that do not appear in corresponding studies of type I vacua.

Original language | English (US) |
---|---|

Article number | 106010 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 73 |

Issue number | 10 |

DOIs | |

State | Published - 2006 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

**Statistics on the heterotic landscape : Gauge groups and cosmological constants of four-dimensional heterotic strings.** / Dienes, Keith R.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Statistics on the heterotic landscape

T2 - Gauge groups and cosmological constants of four-dimensional heterotic strings

AU - Dienes, Keith R

PY - 2006

Y1 - 2006

N2 - Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and nonsupersymmetric string vacua fills out a landscape whose features are largely unknown. It is then hoped that progress in extracting phenomenological predictions from string theory-such as correlations between gauge groups, matter representations, potential values of the cosmological constant, and so forth-can be achieved through statistical studies of these vacua. To date, most of the efforts in these directions have focused on type I vacua. In this note, we present the first results of a statistical study of the heterotic landscape, focusing on more than 105 explicit nonsupersymmetric tachyon-free heterotic string vacua and their associated gauge groups and one-loop cosmological constants. Although this study has several important limitations, we find a number of intriguing features which may be relevant for the heterotic landscape as a whole. These features include different probabilities and correlations for different possible gauge groups as functions of the number of orbifold twists. We also find a vast degeneracy amongst nonsupersymmetric string models, leading to a severe reduction in the number of realizable values of the cosmological constant as compared with naïve expectations. Finally, we find strong correlations between cosmological constants and gauge groups which suggest that heterotic string models with extremely small cosmological constants are overwhelmingly more likely to exhibit the standard model gauge group at the string scale than any of its grand-unified extensions. In all cases, heterotic world sheet symmetries such as modular invariance provide important constraints that do not appear in corresponding studies of type I vacua.

AB - Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and nonsupersymmetric string vacua fills out a landscape whose features are largely unknown. It is then hoped that progress in extracting phenomenological predictions from string theory-such as correlations between gauge groups, matter representations, potential values of the cosmological constant, and so forth-can be achieved through statistical studies of these vacua. To date, most of the efforts in these directions have focused on type I vacua. In this note, we present the first results of a statistical study of the heterotic landscape, focusing on more than 105 explicit nonsupersymmetric tachyon-free heterotic string vacua and their associated gauge groups and one-loop cosmological constants. Although this study has several important limitations, we find a number of intriguing features which may be relevant for the heterotic landscape as a whole. These features include different probabilities and correlations for different possible gauge groups as functions of the number of orbifold twists. We also find a vast degeneracy amongst nonsupersymmetric string models, leading to a severe reduction in the number of realizable values of the cosmological constant as compared with naïve expectations. Finally, we find strong correlations between cosmological constants and gauge groups which suggest that heterotic string models with extremely small cosmological constants are overwhelmingly more likely to exhibit the standard model gauge group at the string scale than any of its grand-unified extensions. In all cases, heterotic world sheet symmetries such as modular invariance provide important constraints that do not appear in corresponding studies of type I vacua.

UR - http://www.scopus.com/inward/record.url?scp=33646886117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646886117&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.73.106010

DO - 10.1103/PhysRevD.73.106010

M3 - Article

AN - SCOPUS:33646886117

VL - 73

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 10

M1 - 106010

ER -