arXiv:hep-th/9708062v1 11 Aug 1997 CERN-TH/97-103, NEIP-97-006 LPTENS/97/24, CPTH-S507.0597 hep-th/9708062 R 2 CORRECTIONS AND NON-PERTURBATIVE DUALITIES OF N = 4 STRING GROUND STATES A. GREGORI 1 , E. KIRITSIS 1 , C. KOUNNAS 1, ∗ , N.A. OBERS 1 , P.M. PETROPOULOS 1, 2, ⋄ and B. PIOLINE 1, ⋄ 1 Theory Division, CERN † 1211 Geneva 23, Switzerland and 2 Institut de Physique Th´ eorique, Universit´ e de Neuchˆ atel 2000 Neuchˆ atel, Switzerland Abstract We compute and analyse a variety of four-derivative gravitational terms in the effective action of six- and 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 K 3. 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 2 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 Th´ eorique de l’Ecole Normale Sup´ erieure, CNRS, 24 rue Lhomond, 75231 Paris Cedex 05, France. ⋄ On leave from Centre de Physique Th´ eorique, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France. † e-mail addresses: agregori, kiritsis, kounnas, obers, petro, bpioline@mail.cern.ch.