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

TL;DR

This paper explores the spectra of $AdS_3$ supergravities related to D1/D5 systems in orbifolded and orientifolded type IIB theories with 16 supercharges, matching supergravity calculations with dual CFT elliptic genera via U-duality.

Contribution

It computes the supergravity elliptic genus for various models and confirms agreement with dual CFT results, testing U-duality in different charge regimes.

Findings

Supergravity elliptic genus matches CFT results in the expected regime.

U-duality exchanges KK momentum and D1 charge, enabling tests in different regimes.

Agreement supports the duality between supergravity spectra and (4,4) CFTs.

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/$\Omega I_4$, 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.