Towering gravitons in AdS3/CFT2

A bstract BPS states in holographic CFTs are usually classified into supergravitons, namely BPS fluctuations around empty AdS, and black-hole microstates, which appear above an energy threshold. In AdS 3 /CFT 2 , however, this picture is incomplete because of additional degrees of freedom, called singletons, associated with boundary diffeomorphisms. We present a general procedure for extending the BPS spectrum of supergravitons by dressing them with singletons, thereby defining a generalized, gravity-sector Hilbert space in CFT that admits a decomposition into affine multiplets of the full superconformal algebra. This extends the procedure previously proposed in [1] which was applicable only at low levels, by removing that limitation. We apply the new procedure to the D1-D5 CFT Sym N ( T 4 ) and explicitly construct affine multiplets in the gravity sector for the N = 2 theory up to level h = 2. We find that, at the free orbifold point, the gravity-sector spectrum agrees with the CFT spectrum up to $$ h=\frac{1}{2} $$ h = 1 2 . Upon turning on a deformation, however, states at h = 1 lift and the agreement improves to $$ h=\frac{3}{2} $$ h = 3 2 . Interestingly, the lifting occurs between states in the gravity sector, involving mixtures of supergravitons and singletons, and stringy states. In the cases we consider we find that, upon deformation, the gravity-sector Hilbert space becomes the monotone Hilbert space while its complement becomes the fortuitous Hilbert space.