D1/D5 systems in ${\cal N}=4$ string theories

TL;DR

This paper constructs conformal field theory descriptions of D1/D5 brane systems in specific type IIB string theory orbifolds, matching two-charge state counts with U-duality predictions and exploring puzzles in three-charge systems.

Contribution

It introduces new CFT models for D1/D5 systems in Z_2 orbifolds and discusses their implications for BPS state counting and U-duality constraints.

Findings

Two-charge state multiplicities match U-duality predictions.

Identifies a puzzle in three-charge BPS state counting.

Suggests RR backgrounds in CFT may resolve the puzzle.

Abstract

We propose CFT descriptions of the D1/D5 system in a class of freely acting Z_2 orbifolds/orientifolds of type IIB theory, with sixteen unbroken supercharges. The CFTs describing D1/D5 systems involve N=(4,4) or N=(4,0) sigma models on $(R^3\times S^1\times T^4\times (T^4)^N/S_N)/Z_2$, where the action of Z_2 is diagonal and its precise nature depends on the model. We also discuss D1(D5)-brane states carrying non-trivial Kaluza-Klein charges. The resulting multiplicities for two-charge bound states are shown to agree with the predictions of U-duality. We raise a puzzle concerning the multiplicities of three-charge systems, which is generically present in all vacuum configurations with sixteen unbroken supercharges studied so far, including the more familiar type IIB on K3 case: the constraints put on BPS counting formulae by U-duality are apparently in contradiction with any CFT interpretation. We argue that the presence of RR backgrounds appearing in the symmetric product CFT may provide a resolution of this puzzle.