Rotating deformations of AdS_3\times S^3, the orbifold CFT and strings in the pp-wave limit

TL;DR

This work extends the holographic dictionary to $AdS_3$×$S^3$×$T^4$ by constructing gravity duals for NS-sector chiral primaries built from orbifold twist operators and by establishing a BMN-like map between string excitations and CFT twist-chain states. The authors derive an Aichelburg–Sexl-type solution and, more robustly, a family of conical-defect geometries whose scalar spectra and travel times reproduce the CFT long-circle physics exactly, linking redshift in gravity to multiple winding in the CFT. A detailed correspondence is developed between string oscillators and CFT operators built atop the building block $\sigma_2^{--}$, with excitations described as oscillations of a Fermi sea on the long circle, offering a cohesive picture of how fast-moving strings in $AdS_3$×$S^3$ map to orbifold CFT dynamics. The analysis covers both the NS orbifold point and the torus ($T^4$) vibrations, arguing that the leading energy scales and operator identifications persist across moduli, thereby generalizing the BMN program to a new holographic setting. Overall, the paper strengthens the link between gravity microstates and chiral primaries in the D1-D5 system and highlights redshift as the gravity-side manifestation of long-circle dynamics in the dual CFT.

Abstract

We construct an exact metric which at short distances is the metric of massless particles in 5+1 spacetime (moving along a diameter of the sphere) and is AdS_3\times S^3 at infinity. We also consider a set of a conical defect spacetimes which are locally AdS_3\times S^3 and have the masses and charges of a special set of chiral primaries of the dual orbifold CFT. We find that excitation energies for a scalar field in the latter geometries agree exactly with the excitations in the corresponding CFT state created by twist operators: redshift in the geometry reproduces `long circle' physics in the CFT. We propose a map of string states in AdS_3\times S^3\times T^4 to states in the orbifold CFT, analogous to the recently discovered map for AdS_5\times S^5. The vibrations of the string can be pictured as oscillations of a Fermi sea in the CFT.