Abstract
We consider four dimensional CHL models with sixteen spacetime supersymmetries obtained from orbifolds of type IIA superstring on K3 x T^2 by a 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 SL(2,Z)-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/Z_N, for some Z_N-symmetry preserving half of the spacetime supersymmetries.
Highlights
Introduction and summaryCHL models are orbifolds of heterotic string theory on T 6 preserving N = 4 supersymmetry, or, equivalently, of type II string theory on K3 × T 2 [1,2,3,4]
We consider four dimensional CHL models with sixteen spacetime supersymmetries obtained from orbifolds of type IIA superstring on K3×T 2 by a ZN symmetry acting non-geometrically on K3
In this paper we show that the symmetry group of CHL models is larger: generically there is an additional strong-weak duality transformation S → −1/(N S) which has so far gone unobserved in the literature
Summary
In this paper we show that the symmetry group of CHL models is larger: generically there is an additional strong-weak duality transformation S → −1/(N S) which has so far gone unobserved in the literature. We call this new transformation Fricke S-duality.. In the following introduction we shall give an overview of our main results and explain in some detail their connection with black hole microstate counting and Mathieu moonshine
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