Gravity Duals Research Articles

Gravitation from optimized computation: Einstein and beyond

A new principle in quantum gravity, dubbed spacetime complexity, states that gravitational physics emerges from spacetime seeking to optimize the computational cost of its quantum dynamics. Thus far, this principle has been realized at the linearized level, in holographic theories with Einstein gravity duals, assuming the so-called ‘Complexity-Volume’ (CV) proposal. We expand on this proof in two significant directions. First, we derive higher-derivative gravitational equations by including appropriate corrections to the CV dictionary. Second, we show semi-classical equations arise by considering the leading bulk quantum corrections to CV. Our proof is valid for two-dimensional dilaton gravities, where the problem of semi-classical backreaction can be solved exactly. However, we argue the principle should hold more generally, leading us to a concrete proposal for bulk complexity of perturbative excited states in arbitrary dimensions. Our results demonstrate the robustness of spacetime complexity as a guiding principle to understand gravity in terms of quantum computation.

Large p SYK from chord diagrams

The p-body SYK model at finite temperature exhibits submaximal chaos and contains stringy-like corrections to the dual JT gravity. It can be solved exactly in two different limits: “large p” SYK 1 ≪ p ≪ N and “double-scaled” SYK N, p → ∞ with λ = 2p2/N fixed. We clarify the relation between the two. Starting from the exact results in the double-scaled limit, we derive several observables in the large p limit. We compute euclidean 2n-point correlators and out-of-time-order four-point function at long lorentzian times. To compute the correlators we find the relevant asymptototics of the Uqsu11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{U}}_q\\left( su\\left(1,1\\right)\\right) $$\\end{document} 6j-symbol.

AdS/BCFT Correspondence and Horndeski Gravity in the Presence of Gauge Fields: Holographic Paramagnetism/Ferromagnetism Phase Transition

AbstractThis paper presents a dual gravity model for a (2+1)‐dimensional system with a limit on finite charge density and temperature, which will be used to study the properties of the holographic phase transition to paramagnetism‐ferromagnetism in the presence of Horndeski gravity terms. In our model, the non‐zero charge density is supported by a magnetic field. As a result, the radius indicates a localized condensate, as the Horndeski gravity parameter is increased, that is represented by γ. Furthermore, such condensate shows quantum Hall‐type behavior. This radius is also inversely related to the total action coefficients of our model. It is observed that increasing the Horndeski parameter decreases the critical temperature of the holographic model and leads to the harder formation of the magnetic moment at the bottom of the black hole. However, when removing the magnetic field, the ferromagnetic material presents a disorder of its magnetic moments, which is observed through the entropy of the system. The authors also found that at low temperatures, spontaneous magnetization and ferromagnetic phase transition.

A generalized dominance ordering for 1/2-BPS states

We discuss a generalized dominance ordering for irreducible representations of the symmetric group Sn with the aim of distinguishing the corresponding states in the 1/2-BPS sector of U(N) Super Yang-Mills theory when a certain finite number of Casimir operators are known. Having knowledge of a restricted set of Casimir operators was proposed as a mechanism for information loss in this sector and its dual gravity theory in AdS5 × S5. It is well-known that the states in this sector are labeled by Young diagrams with n boxes. We propose a generalization of the well-known dominance ordering of Young diagrams. Using this generalization, we posit a conjecture to determine an upper bound for the number of Casimir operators needed to distinguish between the 1/2-BPS states and thus also between their duals in the gravity theory. We offer numerical and analytic evidence for the conjecture. Lastly, we discuss implications of this conjecture when the energy n of the states is asymptotically large.

Aspects of dynamical cobordism in AdS/CFT

The cobordism conjecture implies that consistent theories of Quantum Gravity must admit the introduction of boundaries. We study the dynamical realization of the cobordism conjecture in type IIB in AdS5 × S5, using the existing gravity duals of 4d \U0001d4a9 = 4 SYM with Gaiotto-Witten superconformal boundary conditions (near-horizon limits of D3-branes ending on NS5- and D5-branes). We show that these configurations are, from the 5d perspective, dynamical cobordism solutions which start from an asymptotic AdS5 vacuum and evolve until they hit an end of the world (ETW) brane with AdS4 worldvolume. The latter displays localization of gravity, and provide a completion of the Karch-Randall (KR) AdS branes, in which the backreaction of running scalars replace the KR cusp in the warp factor with a smooth bump. The dynamical scalars are either in the SO(6) invariant AdS5 bulk sector (e.g. describing the S5 size and its shrinking at the cobordism boundary) or brane localized (e.g. the SO(6) SO(3) × SO(3) squashing due to boundary conditions). We introduce a novel double scaling limit which zooms into the ETW brane and makes localization of gravity manifest, and which shows a tantalizing relation with wedge holography. We extend the picture to AdS5 theories with less (super)symmetry, via orbifolds and S-folds, leading to dynamical cobordisms for gravity duals of 4d theories with \U0001d4a9 = 2 and \U0001d4a9 = 3 supersymmetry.

Microscopic entanglement wedges

We study the holographic duality between the free O(N) vector model and higher spin gravity. Conserved spinning primary currents of the conformal field theory (CFT) are dual to spinning gauge fields in the gravity. Reducing to independent components of the conserved CFT currents one finds two components at each spin. After gauge fixing the gravity and then reducing to independent components, one finds two components of the gauge field at each spin. Collective field theory provides a systematic way to map between these two sets of degrees of freedom, providing a complete and explicit identification between the dynamical degrees of freedom of the CFT and the dual gravity. The resulting map exhibits many features expected of holographic duality: it provides a valid bulk reconstruction, it reproduces insights expected from the holography of information and it provides a microscopic derivation of entanglement wedge reconstruction.

An infinite family of w1+∞ invariant theories on the celestial sphere

In this note we determine the graviton-graviton OPE and the null states in any w1+∞ symmetric theory on the celestial sphere. Our analysis shows that there exists a discrete infinite family of such theories. The MHV-sector and the quantum self dual gravity are two members of this infinite family. Although the Bulk Lagrangian description of this family of theories is not currently known to us, the graviton scattering amplitudes in these theories are heavily constrained due to the existence of null states. Presumably they are exactly solvable in the same way as the minimal models of 2-D CFT.

Holographic entanglement entropy and mutual information in deformed field theories at finite temperature

In this paper we have studied the effect of deformation and temperature on holographic entanglement entropy and mutual information between two subsystems in a deformed field theory at finite temperature. The $T\overline{T}$ deformation operator in field theory introduces a cutoff in the dual gravity background. We define different regimes of parameters and calculate the entanglement entropy and mutual information analytically. We observe that temperature and deformation parameter have similar effects on entanglement entropy and mutual information. They both lead to decrease in mutual information or somehow the correlation between the two subsystems. Interestingly we observe the emergence of correction terms in entanglement entropy and mutual information that are universal and do not depend on the scale of the nonlocal operator.

AdS/BCFT with brane-localized scalar field

In this paper, we study the dynamics of end-of-the-world (EOW) branes in AdS with scalar fields localized on the branes as a new class of gravity duals of CFTs on manifolds with boundaries. This allows us to construct explicit solutions dual to boundary RG flows. We also obtain a variety of annulus-like or cone-like shaped EOW branes, which are not possible without the scalar field. We also present a gravity dual of a CFT on a strip with two different boundary conditions due to the scalar potential, where we find the confinement/deconfinement-like transition as a function of temperature and the scalar potential. Finally, we point out that this phase transition is closely related to the measurement-induced phase transition, via a Wick rotation.

Bounding entanglement wedge cross sections

The entanglement wedge cross sections (EWCSs) are postulated as dual gravity probes to certain measures for the entanglement of multiparty systems. We test various proposed inequalities for EWCSs. As it turns out, contrary to expectations, the EWCS is not clearly monogamous nor polygamous for tripartite systems but the results depend on the details and dimensionality of the geometry of the gravity solutions. We propose weaker monogamy relations for dual entanglement measures, which lead to a new lower bound on EWCS. Our work is based on a plethora of gravity backgrounds: pure anti de Sitter spaces, anti de Sitter black branes, those induced by a stack of Dp-branes, and cigar geometries in generic dimension.

Nöther currents, black hole entropy universality and CFT duality in conformal Weyl gravity

In this paper, we study black hole entropy universality within the conformal Weyl gravity paradigm. We do this by first computing the entropy of specific vacuum and non-vacuum solutions, previously unexplored in conformal Weyl gravity via both the Nöther current method and Wald’s entropy formula. For the vacuum case, we explore the near horizon near extremal Kerr metric, which is also a vacuum solution to conformal Weyl gravity and not previously studied in this setting. For the non-vacuum case, we couple the conformal Weyl gravity field equations to a near horizon (linear) [Formula: see text] gauge potential and analyze the respective found solutions. We highlight the non-universality of black hole entropy between our studied black hole solutions of varying symmetries. However, despite non-universality, the respective black hole entropies are in congruence with Wald’s entropy formula for the specific gravity theory. Finally and despite non-universality, we comment on the construction of a near horizon CFT dual to one of our unique non-vacuum solutions. Due to the non-universality, we must introduce a parameter (similarly to entropy calculations in LQG) which we also call [Formula: see text] and relating to the Weyl anomaly coefficient. The construction follows an [Formula: see text] correspondence in the near horizon, which enables the computation of the full asymptotic symmetry group of the chosen non-vacuum conformal Weyl black hole and its near horizon quantum CFT dual. We conclude with a discussion and outlook for future work.

Holographic measurement and quantum teleportation in the SYK thermofield double

According to holography, entanglement is the building block of spacetime; therefore, drastic changes of entanglement will lead to interesting transitions in the dual spacetime. In this paper, we study the effect of projective measurements on the Sachdev-Ye-Kitaev (SYK) model’s thermofield double state, dual to an eternal black hole in Jackiw-Teitelboim (JT) gravity. We calculate the (Renyi-2) mutual information between the two copies of the SYK model upon projective measurement of a subset of fermions in one copy. We propose a dual JT gravity model that can account for the change of entanglement due to measurement, and observe an entanglement wedge phase transition in the von Neumann entropy. The entanglement wedge for the unmeasured side changes from the region outside the horizon to include the entire time reversal invariant slice of the two-sided geometry as the number of measured Majorana fermions increases. Therefore, after the transition, the bulk information stored in the measured subsystem is not entirely lost upon projection in one copy of the SYK model, but rather teleported to the other copy. We further propose a decoding protocol to elucidate the teleportation interpretation, and connect our analysis to the physics of traversable wormholes.

Estimating flow data models of international trade: dual gravity and spatial interactions

This article investigates asymptotic properties of quasi-maximum likelihood (QML) estimates for flow data on the dual gravity model in international trade with spatial interactions (dependence). The dual gravity model has a well-established economic foundation, and it takes the form of a spatial autoregressive (SAR) model. The dual gravity model originates from Behrens et al., but the spatial weights matrix motivated by their economic theory has a feature that violates existing regularity conditions for asymptotic econometrics analysis. By overcoming the limitations of existing asymptotic theory, we show that QML estimates are consistent and asymptotically normal. The simulation results show the satisfactory finite sample performance of the estimates. We illustrate the usefulness of the model by investigating the McCallum “border puzzle” in the gravity literature.

AdS/BCFT from conformal bootstrap: construction of gravity with branes and particles

We initiate a conformal bootstrap program to study AdS3/BCFT2 with heavy excitations. We start by solving the bootstrap equations associated with two-point functions of scalar/non-scalar primaries under the assumption that one-point functions vanish. These correspond to gravity with a brane and a non-spinning/spinning particle where the brane and the particle do not intersect with each other. From the bootstrap equations, we obtain the energy spectrum and the modified black hole threshold. We then carefully analyze the gravity duals and find the results perfectly match the BCFT analysis. In particular, brane self-intersections, which are usually considered to be problematic, are nicely avoided by the black hole formation. Despite the assumption to solve the bootstrap equations, one-point functions of scalar primaries can be non-zero in general. We construct the holographic dual for a non-vanishing one-point function, in which the heavy particle can end on the brane, by holographically computing the Rényi entropy in AdS/BCFT. As a bonus, we find a refined formula for the holographic Rényi entropy, which appears to be crucial to correctly reproduce the boundary entropy term. On the other hand, we explain why one-point functions of non-scalar primaries always vanish from the gravity dual. The non-sensitivity of the solution for the bootstrap equation to the boundary entropy helps us to construct gravity duals with negative tension branes. We also find a holographic dual of boundary primaries.

Dynamical evolution in the D1D5 CFT

It is interesting to ask: how does the radial space direction emerge from the CFT in gauge-gravity duality? In this context we resolve a long-standing puzzle with the gravity duals of two classes of states in the D1D5 CFT. For each class the CFT states are in the untwisted sector, suggesting that the energy gap should be 1/Ry where Ry is the radius of the circle on which the D1D5 CFT is compactified. For one class of states, the gravity dual indeed has exactly this gap, while for the other class, the gravity dual has a very deep throat, leading to an energy gap much smaller than 1/Ry. We resolve this puzzle by showing that for the latter class of states, perturbing the CFT off its free point leads to the formation of a band structure in the CFT. We also explain why such a band structure does not arise for the first class of states. Thus for the case where a deep throat emerges in the gravity description, the dynamics of falling down this throat is described in the CFT as a sequential ‘hopping’ between states all of which have the same energy at the free point; this hopping amplitude converts an integer spaced spectrum into a closely spaced band of energy levels.

Exploring Spatial Patterns of Interurban Passenger Flows Using Dual Gravity Models.

Geographical gravity models can be employed to quantitatively describe and predict spatial flows, including migration flows, passenger flows, daily commuting flows, etc. However, how to model spatial flows and reveal the structure of urban traffic networks in the case of missing partial data is still a problem to be solved. This paper is devoted to characterizing the interurban passenger flows in the Beijing-Tianjin-Hebei region of China using dual gravity models and Tencent location big data. The method of parameter estimation is the least squares regression. The main results are as follows. First, both the railway and highway passenger flows can be effectively described by dual gravity models. A small part of missing spatial data can be compensated for by predicted values. Second, the fractal properties of traffic flows can be revealed. The railway passenger flows follow the gravity scaling law better than the highway passenger flows. Third, the prediction residuals indicate the changing trend of interurban connections in the study area in recent years. The center of gravity of the spatial dynamics has shifted from the Beijing-Tianjin-Tangshan triangle to the Beijing-Baoding-Shijiazhuang axis. A conclusion can be reached that the dual gravity model is an effective tool for analyzing spatial structures and dynamics of traffic networks and flows. Moreover, the model provides a new approach to estimating the fractal dimensions of traffic networks and spatial flow patterns.

Holographic entanglement entropy inequalities beyond strong subadditivity

The vacuum entanglement entropy in quantum field theory provides nonperturbative information about renormalization group flows. Most studies so far have focused on the universal terms, related to the Weyl anomaly in even space-time dimensions, and the sphere free energy F in odd dimensions. In this work we study the entanglement entropy on a sphere of radius R in a large radius limit, for field theories with gravity duals. At large radius the entropy admits a geometric expansion in powers of R; the leading term is the well-known area term, and we also consider the subleading contributions. These terms can be physical, they contain information about the full renormalization group flow, and they reproduce known monotonicity theorems in particular cases. We set up an efficient method for calculating them using the Hamilton-Jacobi equation for the holographic entanglement entropy. We first reproduce the known result for the area term, the coefficient multiplying Rd−2 in the entanglement entropy. We then obtain the holographic result for the Rd−4 term and establish its irreversibility. Finally, we derive the Rd−6 coefficient for holographic theories, and also establish its irreversibility. This result goes beyond what has been proved in quantum field theory based on strong subadditivity, and hints towards new methods for analyzing the monotonicity of the renormalization group in space-time dimensions bigger than four.

Exact Gravity Duals for Simple Quantum Circuits

Holographic complexity proposals have sparked interest in quantifying the cost of state preparation in quantum field theories and its possible dual gravitational manifestations. The most basic ingredient in defining complexity is the notion of a class of circuits that, when acting on a given reference state, all produce a desired target state. In the present work we build on studies of circuits performing local conformal transformations in general two-dimensional conformal field theories and construct the exact gravity dual to such circuits. In our approach to holographic complexity, the gravity dual to the optimal circuit is the one that minimizes an externally chosen cost assigned to each circuit. Our results provide a basis for studying exact gravity duals to circuit costs from first principles.

Zoo of holographic moving mirrors

We systematically study moving mirror models in two-dimensional conformal field theory (CFT). By focusing on their late-time behavior, we separate the mirror profiles into four classes, named type A (timelike) mirrors, type B (escaping) mirrors, type C (chasing) mirrors, and type D (terminated) mirrors. We analytically explore the characteristic features of the energy flux and entanglement entropy for each type and work out their physical interpretation. Moreover, we construct their gravity duals for which end-of-the-world (EOW) branes play a crucial role. Depending on the mirror type, the profiles of the EOW branes show distinct behaviors. In addition, we also provide a criterion that decides whether the replica method in CFTs computes entanglement entropy or pseudo entropy in moving mirror models.

Gravity duals for defect quivers in the Veneziano limit

We construct gravity duals to supersymmetric gauge theories in the presence of unquenched flavor hypermultiplets in the fundamental representation of the gauge group living on the (1+1)-dimensional defect. This configuration is given by the intersection of two sets of D3-branes. Working in the Veneziano limit with large number of colors and flavors we are able to find a closed set of equations describing the dual geometry. We briefly discuss the corresponding solutions for massless flavors as well as in the small flavor limit of massive hypermultiplets. Interestingly, the frac{1}{16} -BPS supergravity solutions, preserving two Poincaré supercharges, are generically only asymptotically anti de-Sitter and the dilaton does not vary with the holographic radial coordinate. This implies that the classical Type IIB supergravity solutions remain trustworthy descriptions for the gauge theories from the deep IR to the far UV.