Exciting AdS Orbifolds

TL;DR

The paper investigates how rotational AdS3×S3 orbifolds $(AdS_3\times S^3)/{\mathbb Z}_N$ correspond to BPS states in the dual spacetime CFT and how twisted sector moduli encode the relative positions of $N$ groups of ${n_5}/{N}$ fivebranes, with a detailed U-duality map to the F1-NS5 system. It analyzes the excitation spectrum, showing that twisted moding reduces gaps by a factor of $N$ and that long-string states dense the spectrum as one approaches the black hole limit, while untwisted modes map to the singlet sector of the fivebrane gauge theory and twisted modes to Cartan moduli; the discussion also links bulk twist fields to CFT twist operators and to multicenter fivebrane geometries. The authors further relate smeared fivebrane sources to CHS/coset CFT descriptions, clarifying how multicenter and conical geometries arise and how D-strings capture off-diagonal fivebrane dynamics. In the BTZ/cosmology context, they explore BTZ as an AdS3 quotient and argue that the associated boundary stress tensor divergences challenge a naive orbifold interpretation, highlighting regions with timelike identifications and stressing the need for a boundary CFT treatment to settle the viability of such orbifold cosmologies.

Abstract

The supersymmetric $(AdS_3\times S^3)/Z_N$ orbifold constructed by the authors in hep-th/0106171 is shown to describe AdS fragmentation, where fivebranes are emerging from the F1-NS5 background. The twisted sector moduli of the orbifold are the collective coordinates of groups of $n_5/N$ fivebranes. We discuss the relation between the descriptions of this background as a perturbative string orbifold and as a BPS state in the dual spacetime CFT. Finally, we attempt to apply the lessons learned to the description of BTZ black holes as $AdS_3$ orbifolds and to related big crunch/big bang cosmological scenarios.

Figures (7)

• Figure 1: The spatial configuration of the U-dual string source for $n_5=50$, $N=1$, corresponding to global $AdS_3\times S^3$. The $\tilde{x}_5$ direction is periodically identified to make an $n_5$ times wound string. Smearing the source along $\tilde{x}_5$ generates a ring source in the $\tilde{x}_1$-$\tilde{x}_2$ plane.
• Figure 2: The spatial configuration of a U-dual string source for $n_5=50$, $N=5$, related to $(AdS_3\times S^3)/{\mathbb Z}_5$. The strands are separated slightly for visualization purposes. The actual source for the orbifold puts the strands at finite separation.
• Figure 3: In the actual orbifold, the string source becomes $N$ strings arrayed in a ${\mathbb Z}_N$ symmetric fashion on a circle; here $n_5=50$, and $N=5$. The individual strings have been depicted with different colors and thicknesses for ease of visualization.
• Figure 4: The $(AdS_3\times S^3)/{\mathbb Z}_N$ orbifold geometry covers smoothly onto global $AdS_3\times S^3$. Here we have indicated the slicing of the global space into fundamental domains, with the quotient space being the conically singular geometry. This same covering procedure is involved in computations of twist operators in the $(T^4)^{n_1n_5}/S_{n_1n_5}$ orbifold related to the dual spacetime CFT.
• Figure 5: The fundamental domain of the identification of $AdS_3$ corresponding to a BTZ black hole. The vertical (amber) wavy surfaces are identified by a spacelike translation; also the horizontal (blue) disks are identified by a timelike translation. The identification has surfaces of null identification which intersect the boundary along the thick (black) helices. The intersection of all these surfaces is the spacelike BTZ black hole singularity.