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

TL;DR

This paper analyzes four-derivative gravitational terms in N=4 string ground states, revealing dualities and non-perturbative effects, including instanton contributions and symmetry breaking, across various compactifications.

Contribution

It provides explicit computations of gravitational couplings in N=4 string models and demonstrates their duality relations and non-perturbative effects, including instanton contributions and symmetry breaking patterns.

Findings

Exact CP-even R^2 coupling matches tree-level plus instanton effects.

CP-odd coupling includes one-loop axionic interactions and instanton sums.

Evidence for heterotic models with enhanced supersymmetry at strong coupling.

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 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^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 a.R\wedge 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 \Gamma(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.