Holes In AdS Research Articles

Superconformal indices of 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs and holography

We study the superconformal index of 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 superconformal field theories on S1 ×ωS2 in the Cardy-like limit where the radius of the S1 is much smaller than that of the S2. We show that the first two leading terms in this Cardy-like expansion are dictated by the Bethe Ansatz formulation of the topologically twisted index of the same theory. We apply this relation to 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 holographic superconformal field theories describing the low-energy dynamics of N M2-branes and derive closed form expressions, valid to all orders in the 1/N expansion, for the two leading terms in the Cardy-like expansion of the superconformal index. We also discuss the implications of our results for the entropy of supersymmetric Kerr-Newman black holes in AdS4 and the four-derivative corrections to 4d gauged supergravity.

Exploring Tsallis thermodynamics for boundary conformal field theories in gauge/gravity duality

Inspired by AdS/CFT interpretation Karch and Robinson (2015), we analyze thermodynamics for thermal boundary conformal field theories (CFT) that are dual to four-dimensional charged anti-de Sitter (AdS) black holes embedded in 11-dimensional M-theory-inspired models with AdS4×S7 space–time, employing the framework of Tsallis entropy. The latter is recognized as a nonadditive extension of the Boltzmann–Gibbs entropy that can satisfy the thermodynamic extensivity for black holes. Specifically, we consider AdS black holes in AdS4×S7 spacetime, interpreting the number of M2-branes as a thermodynamic variable. Using the Tsallis entropy enables us to highlight peculiar thermodynamic features, resorting to essential tools such as the chemical potential and Gibbs energy while examining phase transitions along iso-charge partitions. Then, we leveraged a class of geometrothermodynamic formalisms, including Weinhold, Ruppeiner, Quevedo I, and II metrics. Quevedo’s formulations provide richer information about phase transitions than the first two methods. Our study sheds new light on AdS black holes in a thermodynamically proper context, deepening our understanding of the role of non-extensivity in the critical behavior of such complex systems.

Quantum vortices, M2-branes and black holes

We study the partition functions of BPS vortices and magnetic monopole operators, in gauge theories describing N M2-branes. In particular, we explore two closely related methods to study the Cardy limit of the index on S2 × ℝ. The first method uses the factorization of this index to vortex partition functions, while the second one uses a continuum approximation for the monopole charge sums. Monopole condensation confines most of the N2 degrees of freedom except N32\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {N}^{\\frac{3}{2}} $$\\end{document} of them, even in the high temperature deconfined phase. The resulting large N free energy statistically accounts for the Bekenstein-Hawking entropy of large BPS black holes in AdS4 × S7. Our Cardy free energy also suggests a finite N version of the N32\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {N}^{\\frac{3}{2}} $$\\end{document} degrees of freedom.

Large N universality of 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal index and AdS black holes

We study the large N limit of the matrix models associated with the superconformal indices of four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal field theories. We find that for a large class of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal gauge theories, the superconformal indices in the large N limit of such theories are dominated by the ‘parallelogram’ saddle, providing O(N2) free energy for the generic value of chemical potentials. This saddle corresponds to BPS black holes in AdS5 whenever a holographic dual description is available. Our saddle applies to a large class of gauge theories, including ADE quiver gauge theories, and the theories with rank-2 tensor matters. Our analysis works for most N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal gauge theories that admit a suitable large N limit while keeping the flavor symmetry fixed. We also find ‘multi-cut’ saddle points, which correspond to the orbifolded Euclidean black holes in AdS5.

Microstates of Accelerating and Supersymmetric AdS_{4} Black Holes from the Spindle Index.

We provide a first principles derivation of the microscopic entropy of a very general class of supersymmetric, rotating, and accelerating black holes in AdS_{4}. This is achieved by analyzing the large-N limit of the spindle index and completes the construction of the first example of a holographic duality involving supersymmetric field theories defined on orbifolds with conical singularities.

Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography

A Cardy-like regime of the four-dimensional superconformal index has been shown to be governed by ’t Hooft anomalies and to single out a large-N saddle carrying the Bekenstein-Hawking entropy of dual supersymmetric black holes in AdS5. For the universal index where no flavour fugacities are turned on, this correspondence has been improved by matching the first subleading corrections to the saddle-point action with the four-derivative corrections to the black hole action in minimal gauged supergravity, as well as the respective corrected entropies. Here, we extend this match by including flavour symmetries. We consider five-dimensional gauged supergravity with vector multiplet and four-derivative couplings, and provide an effective theory reproducing the ’t Hooft anomalies of the R- and flavour symmetries of generic holographic superconformal field theories at next-to-leading order in the large-N expansion. Then we focus on a specific model dual to ℂ3/ℤν quiver gauge theories, where the ’t Hooft anomaly coefficients receive simple but sufficiently generic corrections. In this model, we evaluate the four-derivative corrections to the on-shell action of the supersymmetric multi-charge black hole, showing agreement with the flavoured Cardy-like formula from the index. We give a prediction for the corrected entropy of the supersymmetric black hole and discuss the general validity of our results. Taking the limit of infinite AdS5 radius, we also obtain four-derivative corrections to the action and entropy of supersymmetric asymptotically flat black holes.

Matrix models from black hole geometries

Supersymmetric, magnetically charged (and possibly accelerating) black holes in AdS4 that uplift on Sasaki-Einstein manifolds Y7 to M-theory have a dual matrix model description. The matrix model in turn arises by localization of the 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs, dual to the AdS4 vacuum, on the black hole horizon geometry, which is a Riemann surface Σg (or a spindle Σ). We identify the imaginary part t of the continuously distributed eigenvalues in the matrix model, and their density function ρ(t), with natural geometric quantities associated with the M-theory circle action U(1)M on the near-horizon geometry AdS2 × Y9, the internal space Y9 being a Y7 fibration over Σg (or Σ). Moreover, we argue that the points where ρ′(t) is discontinuous match with the classical action of BPS probe M2-branes wrapping AdS2 and the M-theory circle. We illustrate our findings with the ABJM and ADHM theories, whose duals have Y7 = S7/ℤk, and some of their flavoured variants corresponding to other toric Y7.

The pseudospectra of black holes in AdS

We study the stability of quasinormal modes (QNMs) in electrically charged black brane spacetimes that asymptote to AdS by means of the pseudospectrum. Methodologically, we adopt ingoing Eddington-Finkelstein coordinates to cast QNMs in terms of a generalised eigenvalue problem involving a non-selfadjoint operator; this simplifies the computation significantly in comparison with previous results in the literature. Our analysis reveals spectral instability for (neutral) scalar as well as gravitoelectric perturbations. This indicates that the equilibration process of perturbed black branes is sensitive to external perturbations. Particular attention is given on the hydrodynamic modes, which are found to be the least unstable. In contrast with computations in hyperboloidal coordinates, we find that the pseudospectral contour lines cross to the upper half plane. This indicates the existence of pseudo-resonances as well as the possibility of transient instabilities. We also investigate the asymptotic structure of pseudospectral contour levels and we find remarkable universality across all sectors, persistent in the extremal limit.

Localization and attraction

We use equivariant localization to construct off-shell entropy functions for supersymmetric black holes in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2, D = 4 gauged supergravity coupled to matter. This allows one to compute the black hole entropy without solving the supergravity equations of motion and provides a novel generalization of the attractor mechanism. We consider magnetically charged black holes in AdS4 which have an AdS2 × M2 near horizon geometry, where M2 is a sphere or a spindle, and we also obtain entropy functions for ungauged supergravity as a simple corollary. We derive analogous results for black strings and rings in D = 5 supergravity which have an AdS3 × M2 near horizon geometry, and in this setting we derive an off-shell expression for the central charge of the dual \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = (0, 2), d = 2 SCFT.

Large black hole entropy from the giant brane expansion

We show that the Bekenstein-Hawking entropy of large supersymmetric black holes in AdS5 × S5 emerges from remarkable cancellations in the giant graviton expansions recently proposed by Imamura, and Gaiotto and Lee, independently. A similar cancellation mechanism is shown to happen in the exact expansion in terms of free fermions recently put-forward by Murthy. These two representations can be understood as sums over independent systems of giant D3-branes and free fermions, respectively. At large charges, the free energy of each independent system localizes to its asymptotic expansion near the leading singularity. The sum over the independent systems maps their localized free energy to the localized free energy of the superconformal index of U(N) \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 4 SYM. This result constitutes a non-perturbative test of the giant graviton expansion valid at any value of N. Moreover, in the holographic scaling limit N → ∞ at fixed ratio \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{{\ ext{Entropy}}}{{N}^{2}}$$\\end{document}, it recovers the 1/16 BPS black hole entropy by a saddle-point approximation of the giant graviton expansion.

A compendium of logarithmic corrections in AdS/CFT

We study the logarithmic corrections to various CFT partition functions in the context of the AdS4/CFT3 correspondence for theories arising on the worldvolume of M2-branes. We utilize four-dimensional gauged supergravity and heat kernel methods and present general expressions for the logarithmic corrections to the gravitational on-shell action and black hole entropy for a number of different supergravity backgrounds. We outline several subtle features of these calculations and contrast them with a similar analysis of logarithmic corrections performed directly in the eleven-dimensional uplift of a given four-dimensional supergravity background. We find results consistent with AdS/CFT provided that the infinite sum over KK modes on the internal space is regularized in a specific manner. This analysis leads to an explicit expression for the logarithmic correction to the Bekenstein-Hawking entropy of large Kerr-Newmann and Reissner-Nordström black holes in AdS4. Our results also have important implications for effective field theory coupled to gravity in AdS4 and for the existence of scale-separated AdS4 vacua in string theory, which come in the form of new constraints on the field content and mass spectrum of matter fields.

Topology of critical points in boundary matrix duals

Computation of topological charges of the Schwarzschild and charged black holes in AdS in canonical and grand canonical ensembles allows for a classification of the phase transition points via the Bragg-Williams off-shell free energy. We attempt a topological classification of the critical points and the equilibrium phases of the dual gauge theory via a phenomenological matrix model, which captures the features of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 4, SU(N) Super Yang-Mills theory on S3 at finite temperature at large N. With minimal modification of parameters, critical points of the matrix model at finite chemical potential can be classified as well. The topological charges of locally stable and unstable dynamical phases of the system turn out to be opposite to each other, totalling to zero, and this matches the analysis in the bulk.

Thermodynamic geometry of dyonic black holes in AdS in extended phase space

Ruppeiner scalar curvature can be considered as an empirical tool to explore the nature of interaction among the microstructures of black holes. In the extended phase space, the phase transitions and criticality are investigated for the dyonic black holes in an ensemble, where the electric potential [Formula: see text] is fixed. At first, we described the thermodynamic properties of dyonic black holes to investigate the [Formula: see text] criticality. Further, the Ruppeiner scalar curvature is calculated in an ensemble with fixed [Formula: see text] utilizing the fluctuation coordinates [Formula: see text]. The behavior of interactions among the microstructures of the dyonic black holes in AdS is studied where the dominance of attractive or repulsive interaction is found to be dependent on the values of electric potential [Formula: see text].

Supersymmetric Cardy formula and the Weak Gravity Conjecture in AdS/CFT

The Weak Gravity Conjecture (WGC) in anti-de Sitter spacetime (AdS) asserts the existence of an operator in the boundary conformal field theory (CFT) whose scaling dimension-to-charge ratio satisfies a certain upper bound. This bound is specified by the ratio of the conformal central charge c and the flavor central charge kF. We propose a modified bound in AdS5/CFT4, determined by a combination of two central charges 3c − 2a instead of c. This combination arises in the Cardy-like limit of the 4d superconformal index, which captures the Bekenstein-Hawking entropy of large BPS black holes in AdS5. Using the new bound, we find that certain superconformal field theories (SCFTs) that are previously thought to violate the AdS WGC, including SQCDs in the conformal window, do satisfy the WGC. We check this version of the WGC against all possible superconformal gauge theories with SU(N) gauge group admitting a large N limit when the superpotential is absent. We conjecture the modified version of the WGC is a generic property of any 4d SCFT, regardless of the existence of a weakly coupled gravity dual or a large N limit.

Exact QFT duals of AdS black holes

We construct large N saddle points of the matrix model for the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 Yang- Mills index dual to the BPS black holes in AdS5 × S5, in two different setups. When the two complex chemical potentials for the angular momenta are collinear, we find linear eigenvalue distributions which solve the large N saddle point equation. When the chemical potentials are not collinear, we find novel solutions given by areal eigenvalue distributions after slightly reformulating the saddle point problem. We also construct a class of multi-cut saddle points, showing that they sometimes admit nontrivial filling fractions. As a byproduct, we find that the Bethe ansatz equation emerges from our saddle point equation.

Gravitational Blocks, Spindles and GK Geometry

We derive a gravitational block formula for the supersymmetric action for a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS_3 solutions of type IIB supergravity, sourced by D3-branes, and supersymmetric AdS_2 solutions of D=11 supergravity, sourced by M2-branes. In both cases, the branes are also wrapped over a two-dimensional orbifold known as a spindle, or a two-sphere. We develop various geometric methods for computing the gravitational block contributions, allowing us to recover previously known results for various explicit supergravity solutions, and to significantly generalize these results to other compactifications. For the AdS_3 solutions we give a general proof that our off-shell supersymmetric action agrees with an appropriate off-shell c-function in the dual field theory, establishing a very general exact result in holography. For the AdS_2 solutions our gravitational block formula allows us to obtain the entropy for supersymmetric, magnetically charged and accelerating black holes in AdS_4.

Boundary terms and conserved charges in higher-derivative gauged supergravity

We address some issues in higher-derivative gauged supergravity with Chern-Simons terms, focusing on the five-dimensional case. We discuss the variational problem with Dirichlet boundary conditions as well as holographic renormalization in asymptotically locally AdS spacetimes, and derive the corresponding boundary terms. We then employ Wald’s formalism in order to define conserved charges associated to local symmetries (diffeomorphisms and U(1) gauge transformations), taking into account the effect of generic gauge Chern-Simons terms. We prove that the first law of black hole mechanics and the quantum statistical relation hold in this setup. Chern-Simons terms also lead us to distinguish between Noether charges and Page (or Komar) charges which satisfy the Gauss law. We make use of the latter to compute corrections to the angular momentum and electric charge of the supersymmetric black hole in AdS5 from its corrected near-horizon geometry. This also allows us to derive the microcanonical form of the entropy as a function of the conserved charges relying entirely on the near-horizon geometry. Finally, we comment on four-derivative gauged supergravity in four dimensions, showing that field redefinitions permit to simplify the action at linear order in the corrections, so that the equations of motion are those of the two-derivative theory.

Configuration entropy and instability of accelerating black hole in AdS

We consider the accelerating black hole with a negative cosmological constant in four-dimensional spacetime. There are two configurations such as a black string (BS) phase when a mass parameter is zero and a black hole (BH) phase when a mass parameter is nonzero. We investigate their stability via a configuration entropy (CE). It is found that the BS is not always stable but the BH has a thermally stable range below the critical mass of the BH, which is consistent with thermodynamic instability.

Is the horizon of an eternal black hole really smooth?

We point out that in many eternal black holes, including a Schwarzschild eternal black hole and an eternal black hole in AdS5, instant folded strings are created in the past wedge and render the region just outside the horizon singular. We also make a conjecture regarding instant folded D-branes and discuss their possible implications for eternal black holes. In particular, we argue that the bulk modes responsible for Poincare recurrence, when it occurs in the dual quantum field theory, are either instant folded strings or instant folded D-branes.

A quantum mechanics for magnetic horizons

We construct an mathcal{N} = 2 supersymmetric gauged quantum mechanics, by starting from the 3d Chern-Simons-matter theory holographically dual to massive Type IIA string theory on AdS4× S6, and Kaluza-Klein reducing on S2 with a background that is dual to the asymptotics of static dyonic BPS black holes in AdS4. The background involves a choice of gauge fluxes, that we fix via a saddle-point analysis of the 3d topologically twisted index at large N. The ground-state degeneracy of the effective quantum mechanics reproduces the entropy of BPS black holes, and we expect its low-lying spectrum to contain information about near-extremal horizons. Interestingly, the model has a large number of statistically-distributed couplings, reminiscent of SYK models.