R^2 Corrections and Non-perturbative Dualities of N=4 String ground states

We compute and analyse a variety of four-derivative gravitational terms in the effective action of sixand four-dimensional type II string ground states with N = 4 supersymmetry. In six dimensions, we compute the relevant perturbative corrections for the type II string compactified on K3. In four dimensions we do analogous computations for several models with (4, 0) and (2, 2) supersymmetry. Such ground states are related by heterotic–type II duality or type II–type II U -duality. Perturbative computations in one member of a dual pair give a non-perturbative result in the other member. In particular, the exact CP-even R coupling on the (2, 2) side reproduces the tree-level term plus NS 5-brane instanton contributions on the (4, 0) side. On the other hand, the exact CP-odd coupling yields the one-loop axionic interaction aR ∧ R together with a similar instanton sum. In a subset of models, the expected breaking of the SL(2, Z)S S-duality symmetry to a Γ(2)S subgroup is observed on the non-perturbative thresholds. Moreover, we present a duality chain that provides evidence for the existence of heterotic N = 4 models in which N = 8 supersymmetry appears at strong coupling. CERN-TH/97-103, NEIP-97-006 LPTENS/97/24, CPTH-S507.0597 August 1997 ∗ On leave from Laboratoire de Physique Théorique de l’Ecole Normale Supérieure, CNRS, 24 rue Lhomond, 75231 Paris Cedex 05, France. ⋄ On leave from Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France. † e-mail addresses: agregori, kiritsis, kounnas, obers, petro, bpioline@mail.cern.ch.