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Eight-dimensional non-geometric heterotic strings and enhanced gauge groups

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Abstract

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 \(\mathfrak {e}_8\oplus \mathfrak {e}_7\) 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 \(\mathfrak {e}_8\oplus \mathfrak {e}_7\) 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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Notes

  1. Discussion of connections \(O^+(\Lambda ^{2,2})\)-modular forms and non-geometric heterotic strings can be found in [28]. Non-geometric type II theories were studied in [5, 10].

  2. An elliptic K3 surface degenerates into two 1/2 K3 surfaces intersecting along an elliptic curve in the stable degeneration limit. The duality relation of heterotic strings and F-theory becomes rigorous when the stable degeneration limit is considered on the F-theory side.

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Acknowledgements

We would like to thank Shigeru Mukai for discussions.

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  1. International Research Frontiers Initiative, Tokyo Institute of Technology, Nagatsuta-cho, Midori-ku, Yokohama, Kanagawa, 2268503, Japan

    Yusuke Kimura

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Kimura, Y. Eight-dimensional non-geometric heterotic strings and enhanced gauge groups. Eur. Phys. J. Spec. Top. 232, 3697–3704 (2023). https://doi.org/10.1140/epjs/s11734-023-00889-3

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