Branes and Antibranes in AdS$_3$: The Impossible States in the CFT Gap

TL;DR

The paper constructs explicit type IIB supergravity solutions describing bound states of branes and antibranes in AdS$_3\times$(S$^3$/\mathbb{Z}_{N_k})\times$T$^4$ that match the energy and charges of non-extremal four-charge black holes. These bound states consist of two extremal D1-D5-P holes of opposite signs separated by a Taub-bolt bubble carrying KKm flux, and they are regular outside horizons despite being non-supersymmetric. Strikingly, the lowest-energy bound states lie within the dual CFT mass gap, suggesting a dense, non-perturbative subgap sector that challenges conventional wisdom about gap structure; the entropies of these states are substantial and comparable to halves of the BTZ entropy. The authors analyze stability, finite-temperature deformations, and two possible resolutions to reconcile the subgap states with unitarity and holography: quantum Schwarzian lifting of the throat and higher-genus corrections in the JT/SJT framework. Overall, the work provides explicit, backreacted realizations of intricate, non-perturbative excited states in holographic CFTs and prompts further investigation into their quantum stability and holographic interpretation.

Abstract

We construct a new family of type IIB supergravity solutions corresponding to states of the D1-D5-P-KKm system that carry the same charges and energy as the non-extremal four-charge black hole and are asymptotic to AdS$_3 \times ($S$^3/\mathbb{Z}_{N_k}) \times$ T$^4$. The solutions consist of static binaries of two extremal D1-D5-P black holes with S$^3$ horizons and charges of opposite signs, held in equilibrium by a topological bubble supporting $N_k$ units of KKm charge. Although dynamically unstable, the spacetimes remain smooth on and outside the horizons. The equilibrium condition discretizes the black hole separation, producing a quantized spectrum labeled by the number of antibranes and antimomenta at the anti-BPS center. Strikingly, the lowest-energy states lie within an energy window smaller than the dual CFT mass gap. We also show that these solutions admit regular finite-temperature deformations, which slightly lift the two black holes above extremality while remaining within the gap. These results challenge the expectation that no states exist within the CFT gap, realizing \emph{impossible states}. We discuss two possible resolutions. First, Schwarzian-type quantum corrections could lift these solutions above the gap. Alternatively, though less likely, higher-genus corrections to the two-dimensional effective super-JT theory allow a sparse spectrum of exponentially suppressed states within the gap. In either case, our construction provides explicit realization of a dense set of intricate, highly non-perturbative, low-energy excited states of holographic CFTs.

Figures (6)

• Figure 1: The bound states formed by a BPS and an anti-BPS Strominger-Vafa black hole in AdS$_3\times$S$^3/\mathbb{Z}_{N_k}\times$T$^4$. These solutions are constructed by adding pairs of branes/antibranes and momenta/antimomenta to the four-charge BPS black hole (left panel). We distinguish between zero-energy bound states, which do not include momentum/antimomentum pairs (middle panel), and positive-energy bound states, which do include antimomenta (right panel).
• Figure 2: Schematic representation of the density of states as a function of the energy above the BPS bound. Left: CFT expectations, featuring a mass gap above the supersymmetric states. Right: inclusion of the quantized spectrum of brane-antibrane bound states, including the "impossible states" populating the gap.
• Figure 3: Spacetime structure of the bound state of two Strominger-Vafa black holes in AdS$_3\times$S$^3/\mathbb{Z}_{N_k}\times$T$^4$, one BPS and one anti-BPS. The black holes are separated by a Taub-bolt of KKm charge $N_k$. The thick lines indicate which direction degenerates on the symmetry axis, while the dots are the black hole loci. The $r^2=0$ locus corresponds to the segment between $-\ell^2/8$ to $\ell^2/8$ on the symmetry axis.
• Figure 4: Spacetime of the bound states of two Strominger-Vafa black holes.
• Figure 5: Geometry of the impossible bound states of D1-D5 branes and $\overline{\text{D1}}$-$\overline{\text{D5}}$ antibranes with P momenta and $\overline{P}$ antimomenta, compared to the BPS four-charge black hole.