Towering Gravitons in AdS$_3$/CFT$_2$

TL;DR

This paper extends the BPS spectrum in AdS$_3$/CFT$_2$ by incorporating singletons, providing a detailed construction of the gravity-sector Hilbert space and analyzing spectrum agreement at different deformation levels.

Contribution

It introduces a generalized procedure to include singletons in the BPS spectrum, overcoming previous low-level limitations, and applies this to the D1-D5 CFT for explicit spectrum analysis.

Findings

Spectrum matches CFT up to h=1/2 at the free orbifold point.

Deformation lifts certain states, improving spectrum agreement to h=3/2.

States involved in lifting include supergravitons, singletons, and stringy states.

Abstract

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 that admits decomposition into affine multiplets of the full superconformal algebra. This extends the procedure previously proposed in arXiv:2505.14888 which was applicable only at low levels, by removing that limitation. We apply the new procedure to the D1-D5 CFT ${\rm Sym}^N(T^4)$ 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 up to $h=\frac12$. Upon turning on a deformation, however, states at $h=1$ lift and the agreement improves to $h=\frac32$. Interestingly, the lifting occurs between states in the gravity sector, involving mixtures of supergravitons and singletons, and stringy states. We conjecture that, upon deformation, the gravity-sector Hilbert space becomes the monotone Hilbert space while its complement becomes the fortuitous Hilbert space.