BPS states and supersymmetric index in N=2 type I string vacua

TL;DR

This paper investigates the moduli dependence of certain couplings in N=2 type I string compactifications, using a supersymmetric index related to BPS states, and computes specific one-loop couplings in K3 orientifold models.

Contribution

It introduces a method to determine the supersymmetric index as a function of BPS spectrum in generic models and applies it to compute one-loop moduli dependence of specific couplings.

Findings

Explicit computation of the index for generic models.

Demonstration of moduli dependence of $F_g W^{2g}$ couplings.

Application to Gimon-Johnson K3 orientifold models.

Abstract

We study the moduli dependence of a class of couplings in $K3\times T^2$ compactifications of type I string theory, for which one-loop amplitudes can be written in terms of an N=2 supersymmetric index. This index is determined for generic models as a function of the BPS spectrum. As an application we compute the one-loop moduli dependence of the $F_g W^{2g}$ couplings, where W is the N=2 gravitational superfield, for type I compactifications based on the Gimon-Johnson K3 orientifolds, showing explicitly their dependence on the aforementioned index.