BPS Spectra and Non--Perturbative Couplings in N=2,4 Supersymmetric String Theories

TL;DR

Cardoso, Curio, Lüst, Mohaupt, and Rey analyze BPS spectra in $D=4$, $N=4$ heterotic string compactifications and show that intermediate $N=4$ states can become short in $N=2$ truncations, enabling an $S$-$T$ exchange symmetry in the $N=2$ theory. They develop a unified framework of BPS sums and duality orbits for both $N=4$ and $N=2$ sectors, derive the 1-loop and non-perturbative structure of gravitational couplings, and demonstrate how an exchange symmetry can determine non-perturbative corrections in certain chambers. The work establishes that the holomorphic $N=2$ gravitational function ${ m extcal F}_{grav}$ corresponds to a non-perturbative sum over BPS states and connects it to Type II topological data via string dualities, while showing that in $N=4$ there are no perturbative thresholds and that holomorphic/non-holomorphic free energies encode duality-consistent information. Through explicit analysis of $P_{1,1,2,2,6}(12)$ and $P_{1,1,2,8,12}(24)$ models, the authors illustrate how $S$-$T$ exchange can constrain non-perturbative physics and guide computation of gravitational threshold corrections in strongly coupled regimes. Overall, the paper clarifies how BPS spectra, dualities, and topological data jointly shape non-perturbative gravitational couplings in $N=2,4$ string theories and provides practical tools for evaluating these effects across moduli-space chambers.

Abstract

We study the BPS spectrum in $D=4, N=4$ heterotic string compactifications, with some emphasis on intermediate $N=4$ BPS states. These intermediate states, which can become short in $N=2$ compactifications, are crucial for establishing an $S-T$ exchange symmetry in $N=2$ compactifications. We discuss the implications of a possible $S-T$ exchange symmetry for the $N=2$ BPS spectrum. Then we present the exact result for the 1-loop corrections to gravitational couplings in one of the heterotic $N=2$ models recently discussed by Harvey and Moore. We conjecture this model to have an $S-T$ exchange symmetry. This exchange symmetry can then be used to evaluate non-perturbative corrections to gravitational couplings in some of the non-perturbative regions (chambers) in this particular model and also in other heterotic models.