AdS/CFT correspondence and D1/D5 systems in theories with 16 supercharges

TL;DR

This work extends AdS$_3$/CFT tests to D1/D5 systems in freely acting IIB orbifolds/orientifolds with 16 supercharges, focusing on three models obtained by pairing orbifold/orientifold actions with a transverse shift. By performing a Kaluza-Klein reduction of six-dimensional ${\cal N}=(2,2)$ supergravity on $AdS_3\times S^3$ and incorporating a degree grading, the authors construct the supergravity spectrum and elliptic genus, then compare with boundary CFT data related by U-duality. They find exact agreement for the two-charge sector in the $(4,4)$ models and show that, for the $(4,0)$ cases, gravity data align with the U-dual $(4,4)$ CFT under a $P\leftrightarrow Q_1$ exchange rather than with the naive symmetric-product CFT proposals. The results reinforce the validity of the $(4,4)$ symmetric-product CFTs and illuminate the duality structure connecting different RR backgrounds, while suggesting the need for a distinct $(4,0)$ boundary CFT to fully capture the gravity results in all moduli regimes.

Abstract

We discuss spectra of $AdS_3$ supergravities, arising in the near horizon geometry of D1/D5 systems in orbifolds/orientifolds of type IIB theory with 16 supercharges. These include models studied in a recent paper (hep-th/0012118), where the group action involves also a shift along a transversal circle, as well as IIB/$ΩI_4$, which is dual to IIB on $K3$. After appropriate assignements of the orbifold group eigenvalues and degrees to the supergravity single particle spectrum, we compute the supergravity elliptic genus and find agreement, in the expected regime of validity, with the elliptic genus obtained using U-duality map from (4,4) CFTs of U-dual backgrounds. Since this U-duality involves the exchange of KK momentum $P$ and D1 charge $N$, it allows us to test the (4,4) CFTs in the $P < N/4$ and $N < P/4$ regimes by two different supergravity duals.