Abstract
Only four \( {\mathbbm{T}}^2/{\mathbb{Z}}_K \) orbifold building blocks are admissible in heterotic string compactifications. We investigate the flavor properties of all of these building blocks. In each case, we identify the traditional and modular flavor symmetries, and determine the corresponding representations and (fractional) modular weights of the available massless matter states. The resulting finite flavor symmetries include Abelian and non-Abelian traditional symmetries, discrete R symmetries, as well as the double-covered finite modular groups (S3 × S3) ⋊ ℤ4, T ′, 2D3 and S3 × T ′. Our findings provide restrictions for bottom-up model building with consistent ultraviolet embeddings.
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Acknowledgments
It is a pleasure to thank Xiang-Gan Liu and Michael Ratz for enlightening discussions. A.B. was partially supported by the Deutsche Forschungsgemeinschaft (SFB1258). A.B. and S.R.-S. are supported by UNAM-PAPIIT IN113223 and Marcos Moshinsky Foundation. The authors are grateful to the Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA+ (project ID 390831469), for its hospitality and support during the completion of this work.
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Baur, A., Nilles, H.P., Ramos–Sánchez, S. et al. The eclectic flavor symmetries of \( {\mathbbm{T}}^2/{\mathbb{Z}}_K \) orbifolds. J. High Energ. Phys. 2024, 159 (2024). https://doi.org/10.1007/JHEP09(2024)159
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DOI: https://doi.org/10.1007/JHEP09(2024)159