https://doi.org/10.1140/epjs/s11734-023-00889-3
Review
Eight-dimensional non-geometric heterotic strings and enhanced gauge groups
International Research Frontiers Initiative, Tokyo Institute of Technology, Nagatsuta-cho, Midori-ku, 2268503, Yokohama, Kanagawa, Japan
Received:
30
May
2022
Accepted:
15
May
2023
Published online:
22
June
2023
Some constructions in string theory are linked to noncommutative geometry. Non-geometric strings are among such constructions. Non-geometric strings are related to a noncommutative torus. In this article, we discuss some aspects of non-geometric heterotic strings. We review the construction of eight-dimensional (8D) non-geometric heterotic strings, proposed by Malmendier and Morrison, which do not allow for a geometric interpretation. In the construction, the 
gauge algebra is unbroken. The moduli space of 8D non-geometric heterotic strings and theories arising in the moduli space can be analyzed by studying the geometries of elliptically fibered K3 surfaces with a global section by applying F-theory/heterotic duality. In addition, we review the results of the points in the 8D non-geometric heterotic moduli with the unbroken gauge algebra, at which the non-Abelian gauge groups are maximally enhanced. At these points, the gauge groups formed in the theories do not allow for a perturbative interpretation of the heterotic perspective. However, from the dual F-theory perspective, the K3 geometries at these points are deformations of the stable degenerations that arise from the coincident 7-branes. On the heterotic side, these enhancements can be understood as a non-perturbative effect of 5-brane insertions.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
