Abstract
This work is the second of a series of papers devoted to revisiting the properties of Heterotic string compactifications on ALE spaces. In this project we study the geometric counterpart in F-theory of the T-dualities between Heterotic ALE instantonic Little String Theories (LSTs) extending and generalising previous results on the subject by Aspinwall and Morrison. Since the T-dualities arise from a circle reduction one can exploit the duality between F-theory and M-theory to explore a larger moduli space, where T-dualities are realised as inequivalent elliptic fibrations of the same geometry. As expected from the Heterotic/F-theory duality the elliptic F-theory Calabi-Yau we consider admit a nested elliptic K3 fibration structure. This is central for our construction: the K3 fibrations determine the flavor groups and their global forms, and are the key to identify various T-dualities. We remark that this method works also more generally for LSTs arising from non-geometric Heterotic backgrounds. We study a first example in detail: a particularly exotic class of LSTs which are built from extremal K3 surfaces that admit flavor groups with maximal rank 18. We find all models are related by a so-called T-hexality (i.e. a 6-fold family of T-dualities) which we predict from the inequivalent elliptic fibrations of the extremal K3.
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Acknowledgments
We thank Andreas Braun, Jonathan Heckmann, Joseph Minahan, Thorsten Schimannek and Timo Weigand for discussions. The work of MDZ, PK and ML has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 851931). MDZ also acknowledges support from the Simons Foundation Grant # 888984 (Simons Collaboration on Global Categorical Symmetries). PK has also received funding from the NSF CAREER grant PHY-1848089. PK also thanks the Cornell group for hospitality during the completion of this work.
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Del Zotto, M., Liu, M. & Oehlmann, PK. Back to heterotic strings on ALE spaces. Part II. Geometry of T-dual little strings. J. High Energ. Phys. 2024, 109 (2024). https://doi.org/10.1007/JHEP01(2024)109
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DOI: https://doi.org/10.1007/JHEP01(2024)109