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Abstract We use perturbation theory to construct a family of time-dependent microstrata: a set of non-extremal solutions of IIB supergravity asymptotic to AdS3 × S 3 × T 4. Our construction shows that the “special locus” constraints of [1] can be broken by allowing the solutions to depend on time. We study the secular terms appearing in the perturbation theory. Some of them can be resummed into frequency shifts, with the same interpretation as for the previously-studied microstrata solutions. Other secular terms appear harder to resum, questioning the long-term stability of the solutions.

Abstract Microstrata are the non-extremal analogues of superstrata: they are smooth, non-extremal (non-BPS) solitonic solutions to IIB supergravity whose deep-throat limits approximate black holes. Using perturbation theory and numerical methods, we construct families of solutions using a consistent truncation to three-dimensional supergravity. The most general families presented here involve two continuous parameters, or amplitudes, and four quantized parameters that set the angular momenta and energy levels. Our solutions are asymptotic to the vacuum of the D1-D5 system: AdS3 × S 3 × 𝕋4. Using holography, we show that the they are dual to multi-particle states in the D1-D5 CFT involving a large number of mutually non-BPS supergravitons and we determine the anomalous dimensions of these states from the binding energies in supergravity. These binding energies are uniformly negative and depend non-linearly on the amplitudes of the states. In one family of solutions, smoothness restricts some of the fields to lie on a special locus of the parameter space. Using precision holography we show that this special locus can be identified with the multi-particle states constructed via the standard OPE of the single-particle constituents. Our numerical analysis shows that microstrata are robust at large amplitudes and the solutions can be obtained to very high precision.

Abstract We construct large families of supergravity solutions that are asymptotic to AdS2 and terminate with a cap that is singular in two dimensions but smooth in higher dimensions. These solutions break supersymmetry and conformal invariance. We list arguments suggesting that they correspond to finite-energy excitations in empty AdS2 that back-react on the geometry by inducing non-trivial bubbling topology. They are constructed from the novel technique associated with the Ernst formalism for AdS D × 𝒞 solitons in supergravity [1]. The technique is applied to D = 2 in M-theory with 𝒞 = S3 × T6. The directions of 𝒞 degenerate smoothly as a chain of bolts which ends the spacetime in the IR and generates non-supersymmetric bubbles supported by M2-brane flux. Some specific solutions have “flat” directions where the sizes of their bubbles are totally unconstrained and can be arbitrarily tuned while the asymptotics remains fixed. The solitons should correspond to regular non-supersymmetric states of a holographically dual CFT1.

Abstract The entropy of the three-charge NS5-F1-P black hole in Type IIA string theory comes from the breaking of N 1 F1 strings into N 1 N 5 little strings, which become independent momentum carriers. In M theory, the little strings correspond to strips of M2 brane that connect pairs of parallel M5 branes separated along the M-theory direction. We show that if one takes into account the backreaction of the M-theory little strings on the M5 branes one obtains a maze-like structure, to which one can add momentum waves. We also show that adding momentum waves to the little strings gives rise to a momentum-carrying brane configuration — a super-maze — which locally preserves 16 supercharges. We therefore expect the backreaction of the super-maze to give rise to a new class of horizonless black-hole microstate solutions, which preserve the rotational symmetry of the black-hole horizon and carry 5 / 6 $$ \sqrt{5/6} $$ of its entropy.

Abstract We analyze the BPS equations in the “superstratum sector” of three-dimensional gauged supergravity. We obtain multi-parameter supersymmetric solutions that include elliptical deformations of the supertubes that underlie standard superstrata. We uplift the three-dimensional solutions to obtain the corresponding six-dimensional geometries. This yields new families of elliptically-deformed, ambi-bolar hyper-Kähler geometries in four dimensions with a non-tri-holomorphic U(1) isometry. We also find a new family of scaling superstrata whose S-dual lives entirely within the NS-sector of supergravity, and will thus be more amenable to exact analysis using string probes. In all these new superstrata, including the scaling ones, if the momentum charge is non-zero we find that the ellipse stays away from the degeneration locus in which the ellipse becomes flat.

Abstract We find a two-parameter family of generalized superstrata that emerge as smooth, supersymmetric solutions in three-dimensional gauged supergravity coupled to additional scalar fields. This new family of generalized superstrata are smooth microstate geometries and may be thought of as supersymmetric Coulomb-branch extensions of the original superstrata in which the underlying supertube undergoes an elliptical deformation. These solutions had already been obtained numerically, and as series solutions, to the equations of motion, and some of them were conjectured to be supersymmetric. Here we prove the supersymmetry of an entire two-parameter family and we obtain a highly non-trivial analytic and smooth solution for a one-parameter limit in which the global symmetry of the metric is enhanced to SO(3). We also confirm that the other known families of microstrata are not supersymmetric. We conclude with a cursory analysis of some of the singular brane distributions that can be accessed from three-dimensional gauged supergravity while preserving the same supersymmetries as the superstratum, and therefore of the three-charge black hole.

Abstract By using the approach introduced in Ganchev et al. (Q-Balls Meet Fuzzballs: Non-BPS Microstate Geometries. arXiv:2107.09677 [hep-th]) we construct non-BPS solutions of 6D (1, 0) supergravity coupled to two tensor multiplets as a perturbation of $$\hbox {AdS}_3\times S^3$$ AdS 3 × S 3 . These solutions are both regular and asymptotically $$\hbox {AdS}_3\times S^3$$ AdS 3 × S 3 , so according to the standard holographic framework they must have a dual CFT interpretation as non-supersymmetric heavy operators of the D1–D5 CFT. We provide quantitative evidence that such heavy CFT operators are bound states of a large number of light BPS operators that are mutually non-BPS.

Abstract We construct a three-parameter family of non-extremal microstate geometries, or “microstrata”, that are dual to states and deformations of the D1-D5 CFT. These families are non-extremal analogues of superstrata. We find these microstrata by using a Q-ball-inspired Ansatz that reduces the equations of motion to solving for eleven functions of one variable. We then solve this system both perturbatively and numerically and the results match extremely well. We find that the solutions have normal mode frequencies that depend upon the amplitudes of the excitations. We also show that, at higher order in perturbations, some of the solutions, having started with normalizable modes, develop a “non-normalizable” part, suggesting that the microstrata represent states in a perturbed form of the D1-D5 CFT. This paper is intended as a “Proof of Concept” for the Q-ball-inspired approach, and we will describe how it opens the way to many interesting follow-up calculations both in supergravity and in the dual holographic field theory.

Abstract We analyze the supersymmetry transformations of gauged SO(4) supergravity coupled to extra hypermultiplets in three dimensions, and find large families of smooth BPS solutions that preserve four supersymmetries. These BPS solutions are part of the consistent truncation of some families of six-dimensional superstrata. From the three-dimensional perspective, these solutions give rise to “smoothly-capped BTZ” geometries. We show how the twisting of the spin connection, the holomorphy of the fields, and the Chern-Simons connections all play an essential role in the existence of these supersymmetric solutions. This paper also closes the circle on the consistent truncation of superstrata, showing precisely how every feature of the superstratum enters into the three-dimensional BPS structure.

Abstract Microstate geometries in string theory replace the black-hole horizon with a smooth geometric “cap” at the horizon scale. In geometries constructed using superstratum technology, this cap has the somewhat surprising property that induces very large tidal deformations on infalling observers that are far away from it. We find that this large-distance amplification of the tidal effects is also present in horizonless microstate geometries constructed as bubbling solutions, but can be tamed by suitably arranging the bubbles to reduce the strength of some of the gravitational multipole moments. However, despite this taming, these tidal effects still become large at a significant distance from the microstructure. This result suggests that an observer will not fall unharmed into the structure replacing the black hole horizon.