Abstract
We study structures of solutions for SUSY Minkowski F-term equations on two toroidal orientifolds with h2,1 = 1. Following our previous study [1], with fixed upper bounds of a flux D3-brane charge Nflux, we obtain a whole Landscape and a distribution of degeneracies of physically-distinct solutions for each case. In contrast to our previous study, we consider a non-factorizable toroidal orientifold and its Landscape on which SL(2, ℤ) is violated into a certain congruence subgroup, as it had been known in past studies. We find that it is not the entire duality group that a complex-structure modulus U enjoys but its outer semi-direct product with a “scaling” outer automorphism group. The fundamental region is enlarged to include the |U| < 1 region. In addition, we find that high degeneracy is observed at an elliptic point, not of SL(2, Z) but of the outer automorphism group. Furthermore, ℤ2-enhanced symmetry is realized on the elliptic point. The outer automorphism group is exceptional in the sense that it is consistent with a symplectic basis transformation of background three-cycles, as opposed to the outer automorphism group of SL(2, ℤ). We also compare this result with Landscape of another factorizable toroidal orientifold.
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Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers JP20K14477 (H. O.), JP22J12877 (K. I.), JP23H04512 (H. O.) and JP23K03375 (T. Kobayashi). We would like to thank T. Oikawa for useful comments.
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Ishiguro, K., Kai, T., Kobayashi, T. et al. Flux Landscape with enhanced symmetry not on SL(2, ℤ) elliptic points. J. High Energ. Phys. 2024, 99 (2024). https://doi.org/10.1007/JHEP02(2024)099
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DOI: https://doi.org/10.1007/JHEP02(2024)099