Statistics on the Heterotic Landscape: Gauge Groups and Cosmological Constants of Four-Dimensional Heterotic Strings

TL;DR

This paper presents a pioneering statistical analysis of over 100,000 heterotic string vacua, revealing correlations between gauge groups and cosmological constants, with implications for understanding the heterotic landscape and its phenomenological predictions.

Contribution

First comprehensive statistical study of non-supersymmetric heterotic string vacua, analyzing gauge groups and cosmological constants, highlighting unique features and correlations.

Findings

Different probabilities for gauge groups based on orbifold twists

Severe reduction in possible cosmological constant values due to degeneracy

Models with small cosmological constants favor Standard-Model gauge group

Abstract

Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and non-supersymmetric 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 10^5 explicit non-supersymmetric 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 non-supersymmetric string models, leading to a severe reduction in the number of realizable values of the cosmological constant as compared with naive expectations. Finally, we also 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 worldsheet symmetries such as modular invariance provide important constraints that do not appear in corresponding studies of Type I vacua.