Abstract
We consider four dimensional CHL models with sixteen spacetime supersymmetries obtained from orbifolds of type IIA superstring on K3×T 2 by a \( {\mathrm{\mathbb{Z}}}_N \) symmetry acting (possibly) non-geometrically on K3. We show that most of these models (in particular, for geometric symmetries) are self-dual under a weak-strong duality acting on the heterotic axio-dilaton modulus S by a “Fricke involution” S → −1/NS. This is a novel symmetry of CHL models that lies outside of the standard \( \mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right) \)-symmetry of the parent theory, heterotic strings on T 6. For self-dual models this implies that the lattice of purely electric charges is N-modular, i.e. isometric to its dual up to a rescaling of its quadratic form by N. We verify this prediction by determining the lattices of electric and magnetic charges in all relevant examples. We also calculate certain BPS-saturated couplings and verify that they are invariant under the Fricke S-duality. For CHL models that are not self-dual, the strong coupling limit is dual to type IIA compactified on \( {T}^6/{\mathrm{\mathbb{Z}}}_N \), for some \( {\mathrm{\mathbb{Z}}}_N \)-symmetry preserving half of the spacetime supersymmetries.
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Persson, D., Volpato, R. Fricke S-duality in CHL models. J. High Energ. Phys. 2015, 1–55 (2015). https://doi.org/10.1007/JHEP12(2015)156
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DOI: https://doi.org/10.1007/JHEP12(2015)156