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Exploring the landscape of heterotic strings on T-d

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Font,  Anamaria
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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2007.10358.pdf
(Preprint), 998KB

2020_Article_.pdf
(Publisher version), 2MB

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Citation

Font, A., Fraiman, B., Graña, M., Núñez, C. A., & Parra, H. (2020). Exploring the landscape of heterotic strings on T-d. Journal of High Energy Physics, 2020(10): 194. doi:10.1007/JHEP10(2020)194.


Cite as: http://hdl.handle.net/21.11116/0000-0006-D482-7
Abstract
Compactifications of the heterotic string on T^d are the simplest, yet rich enough playgrounds to uncover swampland ideas: the U(1)^{d+16} left-moving gauge symmetry gets enhanced at special points in moduli space only to certain groups. We state criteria, based on lattice embedding techniques, to establish whether a gauge group is realized or not. For generic d, we further show how to obtain the moduli that lead to a given gauge group by modifying the method of deleting nodes in the extended Dynkin diagram of the Narain lattice II_{1,17}. More general algorithms to explore the moduli space are also developed. For d=1 and 2 we list all the maximally enhanced gauge groups, moduli, and other relevant information about the embedding in II_{d,d+16}. In agreement with the duality between heterotic on T^2 and F-theory on K3, all possible gauge groups on T^2 match all possible ADE types of singular fibers of elliptic K3 surfaces. We also present a simple method to transform the moduli under the duality group, and we build the map that relates the charge lattices and moduli of the compactification of the E_8 x E_8 and Spin(32)/Z_2 heterotic theories.