Fricke S-duality in CHL models

TL;DR

This paper uncovers a novel Fricke involution duality in certain CHL string models, revealing new self-duality properties and modular charge lattices, with implications for BPS couplings and non-self-dual cases.

Contribution

It introduces the Fricke S-duality in CHL models, extending the understanding of dualities beyond standard SL(2,Z) symmetry and characterizes the charge lattices and couplings.

Findings

Most models are self-dual under Fricke involution.

Electric charge lattices are N-modular in self-dual models.

BPS couplings are invariant under Fricke S-duality.

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.