Supersymmetric Black Holes Research Articles

On supersymmetric multipole ratios

Four-dimensional supersymmetric black holes are static and so have all vanishing multipoles (except the mass monopole). Nevertheless, it is possible to define finite multipole ratios for these black holes, by taking the ratio of (finite) multipoles of supersymmetric multicentered geometries and then taking the black hole scaling limit of the multipole ratios within these geometries. An alternative way to calculate these multipole ratios is to deform the supersymmetric black hole slightly into a non-extremal, rotating black hole, calculate the multipole ratios of this altered black hole, and then take the supersymmetric limit of the ratios. Bena and Mayerson observed that for a class of microstate geometries, these two a priori completely different methods give spectacular agreement for the resulting supersymmetric black hole multipole ratios. They conjectured that this agreement is due to the smallness of the entropy parameter for these black holes. We correct this conjecture and give strong evidence supporting a more refined conjecture, which is that the agreement of multipole ratios as calculated with these two different methods is due to both the microstate geometry and its corresponding black hole having a property we call “large dipole”, which can be interpreted as their center of mass being far away from its apparent center.

Phases of mathcal{N} = 2 Sachdev-Ye-Kitaev models

We study mathcal{N} = 2 supersymmetric Sachdev-Ye-Kitaev (SYK) models with com- plex fermions at non-zero background charge. Motivated by multi-charge supersymmetric black holes, we propose a new mathcal{N} = 2 SYK model with multiple U(1) symmetries, integer charges, and a non-vanishing supersymmetric index, realizing features not present in known SYK models. In both models, a conformal solution with a super-Schwarzian mode emerges at low temperatures, signalling the appearance of nearly AdS2/BPS physics. However, in contrast to complex SYK, the fermion scaling dimension depends on the background charge in the conformal limit. For a critical charge, we find a high to low entropy phase transition in which the conformal solution ceases to be valid. This transition has a simple interpretation– the fermion scaling dimension violates the unitarity bound. We offer some comments on a holographic interpretation for supersymmetric black holes.

Root of unity asymptotics for Schur indices of 4d Lagrangian theories

The Schur index of a 4 dimensional mathcal{N} = 2 superconformal field theory counts (with sign) bosonic and fermionic states that preserve 4 supercharges. We consider the Schur indices of 4d mathcal{N} = 4 super Yang-Mills and mathcal{N} = 2 circular quiver gauge theories with gauge groups U(N) or SU(N). We calculate the exponentially dominant part of their asymptotic expansions as the index parameter q approaches any root of unity. We find that some of the indices exhibit “small” ( mathcal{O} (N0) as N → ∞) exponential growth, which is much smaller than an mathcal{O} (N2) exponential growth of states that is indicative of a black hole. This implies that the indices do not capture a growth of states that would correspond to a supersymmetric black hole that preserves 4 supercharges in the holographic dual AdS theory. Interestingly, the exponentially dominant part in the Schur asymptotics we consider, depends on the parity of the rank N.

Operational islands and black hole dissipation in JT gravity

In this work, we revisit the problem of finding entanglement islands in 2d Jackiw-Teitelboim (JT) gravity. We implement the following adjustments to the traditional setup: (1) we do not explicitly couple to a non-gravitating system, instead we implement only pure absorption into a fiducial detector, (2) we utilise the operationally defined renormalised matter entanglement entropy, as defined by the boundary observer’s wordline. We show that this leads to a unitary Page curve that we explicitly compute, with an island outside of the event horizon. Next, we extend the analysis to a charged and/or supersymmetric black hole. We find that in a certain regime the charged black hole grows first as it emits superradiation before eventually dissipating. We obtain similar results when embedding the system in a supersymmetric setting.

Higher derivative corrections and AdS5 black holes

The authors investigate the precise holography between a 5d gauged supergravity and the dual superconformal field theory (CFT) on the 4d boundary. They show that four-derivative contributions to the action of supersymmetric black holes on the supergravity site matches precisely with certain subleading terms in the CFT index which are determined by anomalies.

Supersymmetric Black Holes with a Single Axial Symmetry in Five Dimensions

We present a classification of asymptotically flat, supersymmetric black hole and soliton solutions of five-dimensional minimal supergravity that admit a single axial symmetry which ‘commutes’ with the supersymmetry. This includes the first examples of five-dimensional black hole solutions with exactly one axial Killing field that are smooth on and outside the horizon. The solutions have similar properties to the previously studied class with biaxial symmetry, in particular, they have a Gibbons–Hawking base and the harmonic functions must be of multi-centred type with the centres corresponding to the connected components of the horizon or fixed points of the axial symmetry. We find a large moduli space of black hole and soliton spacetimes with non-contractible 2-cycles and the horizon topologies are S^3, S^1times S^2 and lens spaces L(p, 1).

On the uniqueness of supersymmetric AdS(5) black holes with toric symmetry

We consider the classification of supersymmetric AdS5 black hole solutions to minimal gauged supergravity that admit a torus symmetry. This problem reduces to finding a class of toric Kähler metrics on the base space, which in symplectic coordinates are determined by a symplectic potential. We derive the general form of the symplectic potential near any component of the horizon or axis of symmetry, which determines its singular part for any black hole solution in this class, including possible new solutions such as black lenses and multi-black holes. We find that the most general known black hole solution in this context, found by Chong, Cvetic, Lü and Pope (CCLP), is described by a remarkably simple symplectic potential. We prove that any supersymmetric and toric solution that is timelike outside a smooth horizon, with a Kähler base metric of Calabi type, must be the CCLP black hole solution or its near-horizon geometry.

A note on co-dimension 2 defects in N = 4,d = 7 gauged supergravity

In this note we present a solution of N=4,d=7 gauged supergravity which is holographically dual to a co-dimension two defect living in a six dimensional SCFT. The solution is obtained by double analytic continuation of a two charge supersymmetric black hole solution. The condition that no conical deficits are present in the bulk and on the boundary is satisfied by a one parameter family of solutions for which some holographic observables are computed.

The phase diagram of BPS black holes in AdS5

Motivated by recent studies of supersymmetric black holes, we revisit the phase diagram of AdS black holes, whether BPS or not, with particular emphasis on the role of rotation. We develop BPS thermodynamics systematically and, in many explicit examples, we study its striking similarities with more familiar AdS black holes, as well as some differences. We highlight an important fugacity that preserves BPS saturation but is not captured by the supersymmetric index.

Non-topological logarithmic corrections in minimal gauged supergravity

We compute the logarithmic correction to the entropy of asymptotically AdS4 black holes in minimal mathcal{N} = 2 gauged supergravity. We show that for extremal black holes the logarithmic correction computed in the near horizon geometry agrees with the result in the full geometry up to zero mode contributions, thus clarifying where the quantum degrees of freedom lie in AdS spacetimes. In contrast to flat space, we observe that the logarithmic correction for supersymmetric black holes can be non-topological in AdS as it is controlled by additional four-derivative terms other than the Euler density. The available microscopic data and results in 11d supergravity indicate that the full logarithmic correction is topological, which suggests that the topological nature of logarithmic corrections could serve as a diagnosis of whether a low-energy gravity theory admits an ultraviolet completion.

Quantum entropy of BMPV black holes and the topological M-theory conjecture

We present a formula for the quantum entropy of supersymmetric five-dimensional spinning black holes in M-theory compactified on CY3, i.e., BMPV black holes. We use supersymmetric localization in the framework of off-shell five dimensional N = 2 supergravity coupled to I = 1, . , NV + 1 off-shell vector multiplets. The theory is governed at two-derivative level by the symmetric tensor {mathcal{C}}_{IJK} (the intersection numbers of the Calabi-Yau) and at four-derivative level by the gauge-gravitational Chern-Simons coupling cI (the second Chern class of the Calabi-Yau). The quantum entropy is an NV +2-dimensional integral parameterised by one real parameter φI for each vector multiplet and an additional parameter φ0 for the gravity multiplet. The integrand consists of an action governed completely by {mathcal{C}}_{IJK} and cI, and a one-loop determinant. Consistency with the on-shell logarithmic corrections to the entropy, the symmetries of the very special geometry of the moduli space, and an assumption of analyticity constrains the one-loop determinant up to a scale-independent function g(φ0). For g = 1 our result agrees completely with the topological M-theory conjecture of Dijkgraaf, Gukov, Neitzke, and Vafa for static black holes at two derivative level, and provides a natural extension to higher derivative corrections. For rotating BMPV black holes, our result differs from the DGNV conjecture at the level of the first quantum corrections.

Multicharge accelerating black holes and spinning spindles

We construct a family of multi-dyonically charged and rotating supersymmetric AdS$_2\times \Sigma$ solutions of $D=4$, $\mathcal{N}=4$ gauged supergravity, where $\Sigma$ is a sphere with two conical singularities known as a spindle. We argue that these arise as near horizon limits of extremal dyonically charged rotating and accelerating supersymmetric black holes in AdS$_4$, that we conjecture to exist. We demonstrate this in the non-rotating limit, constructing the accelerating black hole solutions and showing that the non-spinning spindle solutions arise as the near horizon limit of the supersymmetric and extremal sub-class of these black holes. From the near horizon solutions we compute the Bekenstein-Hawking entropy of the black holes as a function of the conserved charges, and show that this may equivalently be obtained by extremizing a simple entropy function. For appropriately quantized magnetic fluxes, the solutions uplift on $S^7$, or its ${\cal N}=4$ orbifolds $S^7/\Gamma$, to smooth supersymmetric solutions to $D=11$ supergravity, where the entropy is expected to count microstates of the theory on $N$ M2-branes wrapped on a spinning spindle, in the large $N$ limit.

Freudenthal duality of near-extremal black holes and Jackiw-Teitelboim gravity

Freudenthal duality (F-duality), an anti-involution of charge vectors, keeps the entropy and attractor solutions invariant for an extremal supersymmetric black hole. We analyze the effect of F-duality on the entropy of a near-extremal STU black hole in $\mathcal{N}=2$ ungauged, four-dimensional supergravity. We consider double-extremal black holes, whose attractor solutions are fixed in terms of the black hole charges throughout the moduli space. It is well known that Jackiw-Teitelboim (JT) gravity governs the dynamics of the near-horizon regions of higher-dimensional, near-extremal black holes. Owing to this fact, we reduce the four-dimensional supergravity theory to two dimensions to construct a JT gravity--like model and compute the near-extremal entropy. We then analyze the effect of F-duality on this entropy. We show that the F-duality breaks down for the case of near-extremal solutions if one considers the duality operation generated through near-extremal entropy rather than the extremal one.

Shockwaves in black hole microstate geometries

Gravitational solutions involving shockwaves have attracted significant recent interest in the context of black holes and quantum chaos. Certain classes of supersymmetric two-charge black hole microstates are described by supergravity solutions containing shockwaves, that are horizonless and smooth away from the shockwave. These configurations have been used to describe how black hole microstates absorb and scramble perturbations. In this paper we construct the first family of asymptotically flat supersymmetric three-charge microstate solutions that contain shockwaves. We identify a family of holographically dual states of the D1-D5 CFT and show that these pass a set of tests, including a precision holographic test. We find precise agreement between gravity and CFT. Our results may prove useful for constructing more general families of black hole microstate solutions.

Growth of the 116 -BPS index in 4d N=4 supersymmetric Yang-Mills theory

We study the microcanonical superconformal index of $\frac{1}{16}$-supersymmetric operators in 4d $\mathcal{N}=4$ $U(N)$ super Yang-Mills (SYM) theory. We show, numerically for $N\ensuremath{\le}10$, that the large-charge asymptotics are consistent with the entropy of supersymmetric black holes in the dual anti de Sitter space. We then prove, using representation theory, that the index agrees precisely with the multigraviton index, when the charge is less than $2(N+1)$, and begins to deviate for larger values of charge. Thus the $U(N)$ SYM index interpolates between multigraviton values at small charges and black hole growth at large charges.

Modularity of supersymmetric partition functions

We discover a modular property of supersymmetric partition functions of supersymmetric theories with R-symmetry in four dimensions. This modular property is, in a sense, the generalization of the modular invariance of the supersymmetric partition function of two-dimensional supersymmetric theories on a torus i.e. of the elliptic genus. The partition functions in question are on manifolds homeomorphic to the ones obtained by gluing solid tori. Such gluing involves the choice of a large diffeomorphism of the boundary torus, along with the choice of a large gauge transformation for the background flavor symmetry connections, if present. Our modular property is a manifestation of the consistency of the gluing procedure. The modular property is used to rederive a supersymmetric Cardy formula for four dimensional gauge theories that has played a key role in computing the entropy of supersymmetric black holes. To be concrete, we work with four-dimensional mathcal{N} = 1 supersymmetric theories but we expect versions of our result to apply more widely to supersymmetric theories in other dimensions.

Instability of supersymmetric black holes via quantum phase transitions

In this paper we prove that the four-dimensional hyperbolic supersymmetric black holes can be unstable in the canonical ensemble. To this end, we work with an infinite class of mathcal{N} = 2 supergravity theories interpolating between all the single dilaton truncations of the SO(8) gauged mathcal{N} = 8 supergravity. Within these models, we study electrically charged solutions of two different kinds: supersymmetric hairy and extremal non-supersymmetric Reissner-Nordström black holes. We consider these solutions within the same canonical ensemble and show that, for suitable choices of the parameters defining the mathcal{N} = 2 model, the supersymmetric solution features a higher free energy than the non-supersymmetric one. In the absence of additional selection rules, this would imply an instability of the supersymmetric configuration, hinting towards a possible supersymmetry breaking mechanism.

Thermodynamics of accelerating and supersymmetric AdS4 black holes

We study the thermodynamics of $AdS_4$ black hole solutions of Einstein-Maxwell theory that are accelerating, rotating, and carry electric and magnetic charges. We focus on the class for which the black hole horizon is a spindle and can be uplifted on regular Sasaki-Einstein spaces to give solutions of $D=11$ supergravity that are free from conical singularities. We use holography to calculate the Euclidean on-shell action and to define a set of conserved charges which give rise to a first law. We identify a complex locus of supersymmetric and non-extremal solutions, defined through an analytic continuation of the parameters, upon which we obtain a simple expression for the on-shell action. A Legendre transform of this action combined with a reality constraint then leads to the Bekenstein-Hawking entropy for the class of supersymmetric and extremal black holes.

Minimal spin deflection of Kerr-Newman and supersymmetric black hole

Recent studies have shown that minimal couplings for massive spinning particles, which in the classical limit reproduce the leading PM Kerr black hole dynamics, leads to an eikonal S-matrix exhibiting spin-entanglement suppression. In this paper we trace this phenomenon to the suppression of spin-flipping components in the S-matrix, known to be the hallmark of minimal coupling in the ultra-relativistic limit. We further generalize the consideration to charged and mathcal{N} = 4 blackholes, demonstrating that in both cases maximal suppression occurs at the extremal limit.

EFT and the SUSY index on the 2nd sheet

The counting of BPS states in four-dimensional \mathcal{N}=1𝒩=1 theories has attracted a lot of attention in recent years. For superconformal theories, these states are in one-to-one correspondence with local operators in various short representations. The generating function for this counting problem has branch cuts and hence several Cardy-like limits, which are analogous to high-temperature limits. Particularly interesting is the second sheet, which has been shown to capture the microstates and phases of supersymmetric black holes in AdS_55. Here we present a 3d Effective Field Theory (EFT) approach to the high-temperature limit on the second sheet. We use the EFT to derive the behavior of the index at orders \beta^{-2},\beta^{-1},\beta^0β−2,β−1,β0. We also make a conjecture for O(\beta)O(β), where we argue that the expansion truncates up to exponentially small corrections. An important point is the existence of vector multiplet zero modes, unaccompanied by massless matter fields. The runaway of Affleck-Harvey-Witten is however avoided by a non-perturbative confinement mechanism. This confinement mechanism guarantees that our results are robust.