Rotating deformations of AdS₃ × S³, the orbifold CFT and strings in the pp-wave limit

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 AdS₃ × S³ at infinity. We also consider a set of a conical defect spacetimes which are locally AdS₃ S³ 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 AdS₃ × S³ × T⁴ to states in the orbifold CFT, analogous to the recently discovered map for AdS₅ × S⁵. The vibrations of the string can be pictured as oscillations of a Fermi sea in the CFT.