Moulting Black Holes

TL;DR

The paper uncovers a new class of supersymmetric, non-Cardy phases in the D1-D5 system, with boundary entropies that can exceed those of BMPV and with bulk two-centered BPS solutions (BMPV+tube or black rings) that match this entropy region. The enigmatic CFT phase arises from splitting the effective string into long and short sectors, yielding $S_{ ext{enigma}}=2\pi\sqrt{N_p\,(N_p+N-J_L)}$, and it is not captured by the elliptic genus, indicating lifting at strong coupling since the bulk entropy remains substantial but typically smaller. The bulk analysis shows that the maximal-entropy configurations are two-centered and related by bulk spectral flow to their CFT counterparts; however, the bulk entropy is typically subleading to the boundary entropy, suggesting a still-protected yet non-elliptic contribution to the microstate count. Together, these results reveal a controlled holographic realization of a black-hole entropy enigma and motivate the search for a new index capable of capturing these enigmatic states, thereby enriching our understanding of black hole microphysics in AdS$_3\times$S$^3$.

Abstract

We find a family of novel supersymmetric phases of the D1-D5 CFT, which in certain ranges of charges have more entropy than all known ensembles. We also find bulk BPS configurations that exist in the same range of parameters as these phases, and have more entropy than a BMPV black hole; they can be thought of as coming from a BMPV black hole shedding a "hair" condensate outside of the horizon. The entropy of the bulk configurations is smaller than that of the CFT phases, which indicates that some of the CFT states are lifted at strong coupling. Neither the bulk nor the boundary phases are captured by the elliptic genus, which makes the coincidence of the phase boundaries particularly remarkable. Our configurations are supersymmetric, have non-Cardy-like entropy, and are the first instance of a black hole entropy enigma with a controlled CFT dual. Furthermore, contrary to common lore, these objects exist in a region of parameter space (between the "cosmic censorship bound" and the "unitarity bound") where no black holes were thought to exist.

Figures (11)

• Figure 1: The "standard lore" but incorrect phase diagram of the D1-D5 system. Above the blue dotted parabola $N_p=J_L^2/4N$ (the cosmic censorship bound) is the BMPV black hole phase (light blue), while below the parabola is the phase of a gas of supergravity particles (gray). The range of $N_p,J_L$ is bounded from below by the unitarity bound (green solid polygon).
• Figure 2: The updated, correct phase diagram of the D1-D5 system for the CFT and bulk (schematic, not to scale). The parameter range corresponds to the red rectangle in Fig. \ref{['fig:old_phase_diag']}. The abbreviation "c.s. bound" refers to the cosmic censorship bound $N_p=J_L^2/4N$. For further explanations, see the text.
• Figure 3: Various states in the Ramond sector of the D1-D5 CFT.
• Figure 4: Three phases at the orbifold point of the D1-D5 CFT.
• Figure 5: Phase diagram of D1-D5 CFT at the orbifold point.