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<p>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<sub>3</sub> × <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mfenced close=")" open="("> <mrow> <msup> <mi>S</mi> <mn>3</mn> </msup> <mo>/</mo> <msub> <mi>ℤ</mi> <msub> <mi>N</mi> <mi>k</mi> </msub> </msub> </mrow> </mfenced> <mo>×</mo> </math></EquationSource> <EquationSource Format="TEX">\( \left({S}^3/{\mathbb{Z}}_{N_k}\right)\times \)</EquationSource> </InlineEquation> T<sup>4</sup>. The solutions consist of static binaries of two extremal D1-D5-P black holes with S<sup>3</sup> horizons and charges of opposite signs, held in equilibrium by a topological bubble supporting <i>N</i><sub><i>k</i></sub> 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.</p><p>These results challenge the expectation that no states exist within the CFT gap, realizing <i>impossible states</i>. 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.</p>

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Branes and antibranes in AdS3: the impossible states in the CFT gap

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  • 发表日期：

    2026年4月9日

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  • Roberto Emparan,
  • Pierre Heidmann

摘要

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 AdS3 × S 3 / ℤ N k × \( \left({S}^3/{\mathbb{Z}}_{N_k}\right)\times \) T4. The solutions consist of static binaries of two extremal D1-D5-P black holes with S3 horizons and charges of opposite signs, held in equilibrium by a topological bubble supporting Nk 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 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.