Fivebrane instantons and higher derivative couplings in type I theory

TL;DR

This work computes non-perturbative D5-brane instanton corrections to ${{\cal R}^2}$ couplings in four-dimensional Type I string vacua with $\mathcal{N}=4$ supersymmetry, expressing the infinite instanton sum through an elliptic index of the effective $Sp(N)$ gauge theory on the D5-branes. In the infrared, the D5-brane worldvolume theory flows to an orbifold CFT whose elliptic genus encodes the spectrum of $1/2$-BPS states and their $1/4$-BPS bound states, with results matching the dual Type IIA one-loop computations on $K3\times T^2$. The analysis confirms that the instanton sums reproduce Type IIA perturbative predictions and extends to higher derivative couplings sensitive to $1/4$-BPS contributions, reinforcing the IIA/Type I duality in $D=4$, and highlighting the D5-brane CFT as a natural framework for BPS spectra in Type I theory. These findings motivate deeper study of D5-brane CFTs and their potential connections to ADS/CFT and the broader landscape of BPS state counting in four dimensions.

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.