Bound States of Type I D-Strings

TL;DR

This work tests the Type I/heterotic duality by analyzing the IR limit of the O(N) gauge theory on N Type I D-strings, showing it flows to an orbifold CFT whose longest-string twisted sector hosts the threshold D-string bound states. The authors compute the elliptic genus of this orbifold, obtaining explicit expressions that reproduce the heterotic spectrum for all charges in the $Γ_{(1,17)}$ lattice and identifying the KK/longitudinal momentum mapping between the two sides. They demonstrate that only the longest-string sector yields normalizable bound states, while shorter sectors correspond to multi-string configurations, consistent with duality predictions. The results provide a microscopic CFT realization of D-string bound states and a nontrivial compatibility check between Type I and heterotic string theories in nine dimensions.

Abstract

We study the infra-red limit of the O(N) gauge theory that describes the low energy modes of a system of $N$ type I D-strings and provide some support to the conjecture that, in this limit, the theory flows to an orbifold conformal theory. We compute the elliptic genus of the orbifold theory and argue that its longest string sector describes the bound states of D-strings. We show that, as a result, the masses and multiplicities of the bound states are in agreement with the predictions of heterotic-type I duality in 9 dimensions, for all the BPS charges in the lattice $Γ_{(1,17)}$.