Fivebrane instantons and higher derivative couplings in type I theory

TL;DR

This paper calculates D-fivebrane instanton corrections to certain couplings in type I string theory using an elliptic index, confirming duality predictions and providing a detailed BPS spectrum analysis.

Contribution

It expresses instanton sums in terms of an elliptic index and matches these with dual type IIA computations, advancing understanding of BPS states and higher derivative couplings.

Findings

Instanton sums match dual type IIA one-loop results.

Explicit computation of the elliptic index in the infrared.

Spectrum of BPS states is fully described by the proposed CFT.

Abstract

We express the infinite sum of D-fivebrane instanton corrections to ${\cal R}^2$ couplings in ${\cal N}=4$ type I string vacua, in terms of an elliptic index counting 1/2-BPS excitations in the effective $Sp(N)$ brane theory. We compute the index explicitly in the infrared, where the effective theory is argued to flow to an orbifold CFT. The form of the instanton sum agrees completely with the predicted formula from a dual one-loop computation in type IIA theory on $K3\times T^2$. The proposed CFT provides a proper description of the whole spectrum of masses, charges and multiplicities for 1/2- and 1/4- BPS states, associated to bound states of D5-branes and KK momenta. These results are applied to show how fivebrane instanton sums, entering higher derivative couplings which are sensitive to 1/4-BPS contributions, also match the perturbative results in the dual type IIA theory.