Two-dimensional Gravity Research Articles

Two-dimensional (bi-)scalar gravities from four-dimensional Horndeski

Abstract We develop a classical two-dimensional bi-scalar gravity based on the Kaluza–Klein reduction applied to the four-dimensional Horndeski theory. One of the scalar fields arises from the original four-dimensional theory, while the extra scalar emerges from the reduction process. We also introduce a two-dimensional bi-scalar identity that allows for a more concise and elegant reformulation of the resulting bi-scalar Lagrangian. Additionally, we study the linear perturbations around a static background to demonstrate that the bi-scalar theory may support a single healthy propagating mode. Furthermore, by restricting the scalar fields, we investigate a general single scalar theory that is identical to the two-dimensional Horndeski theory up to a boundary term. Our results provide a framework to map a generic two-dimensional dilaton gravity into four-dimensional Horndeski theory.

Remarks on 2D quantum cosmology

We consider two-dimensional quantum gravity endowed with a positive cosmological constant and coupled to a conformal field theory of large and positive central charge. We study cosmological properties at the classical and quantum level. We provide a complete ADM analysis of the classical phase space, revealing a family of either bouncing or big bang/crunch type cosmologies. At the quantum level, we solve the Wheeler-DeWitt equation exactly. In the semiclassical limit, we link the Wheeler-DeWitt state space to the classical phase space. Wavefunctionals of the Hartle-Hawking and Vilenkin type are identified, and we uncover a quantum version of the bouncing spacetime. We retrieve the Hartle-Hawking wavefunction from the disk path integral of timelike Liouville theory. To do so, we must select a particular contour in the space of complexified fields. The quantum information content of the big bang cosmology is discussed, and contrasted with the de Sitter horizon entropy as computed by a gravitational path integral over the two-sphere.

Insights into the crustal and the magmatic feeding structure at the Payunia Volcanic Province highlighted by geophysical methods, in the retroarc of the Southern Central Andes

The Payunia Volcanic Province is a Quaternary volcanic plateau emplaced in the retroarc area in the northern Neuquén Mesozoic Basin, associated with a hydrocarbon system. At deeper levels, this basin is linked to different intrusive systems that developed in the retroarc region at different times, during the Jurassic, Cretaceous, Eocene, Miocene, and even the Quaternary which influenced the hydrocarbon system maturity. We analyzed the Moho structure through this retroarc region, as well as the crustal structure affected by different stages of regional extension. From continuous seismic noise data, we calculated the autocorrelograms to obtain the reflection response below each seismological station. This allowed imaging the surface of primary crustal reflectors and in a few stations the top of an asthenospheric anomaly (SWAP) found by magnetotelluric survey and in concordance with satellite magnetic data. The crustal reflectors were identified in all stations at a mean two-way travel time of about ∼8.5 s and ∼12.5 s using frequency bands of about 1.0–2.4 Hz. Therefore, this is the first geophysical research that estimates the depth of the magmatic system, hosted at the top of the lower crust and the Moho discontinuity. The deepest reflector, only recognized in 4 stations, was observed with a two-way travel time of 17.2 s to 19.6 s. We used a mean one-dimensional Vp model to obtain the corresponding reflector depths which constrain the two-dimensional forward gravity model that fits with the observed regional anomaly for the region. We finally established a relationship between the shallowest sublithospheric electrical conductivity anomalies determined in previous researches and the strong deep reflections observed in some of the seismological stations. This information may help to constrain geochemical and petrological models and re-evaluate the hydrocarbon system maturity of the northern Neuquén basin.

Curvature correlators in nonperturbative 2D Lorentzian quantum gravity

Correlation functions are ubiquitous tools in quantum field theory from both a fundamental and a practical point of view. However, up to now their use in theories of quantum gravity beyond perturbative and asymptotically flat regimes has been limited, due to difficulties associated with diffeomorphism invariance and the dynamical nature of geometry. We present an analysis of a manifestly diffeomorphism-invariant, nonperturbative two-point curvature correlator in two-dimensional Lorentzian quantum gravity. It is based on the recently introduced quantum Ricci curvature and uses a lattice regularization of the full path integral in terms of causal dynamical triangulations. We discuss some of the subtleties and ambiguities in defining connected correlators in theories of dynamical geometry, and provide strong evidence from Monte Carlo simulations that the connected two-point curvature correlator in 2D Lorentzian quantum gravity vanishes. This work paves the way for an analogous investigation in higher dimensions.

The subsurface anatomy of a mid-upper crustal magmatic intrusion zone beneath the Boku volcanic complex, Main Ethiopian Rift inferred from gravity data

Strain accommodation in the Main Ethiopian Rift has been localized since the Quaternary in axial magmatic segments that contain magma intrusion, volcanic complexes, and fault zones. However, the crustal structure and magmatic plumbing features of the individual volcanic complexes within these magmatic segments are poorly constrained. In this study, gravity data from the Global Gravity Model plus2013 was used to interpret the crustal structure and subsurface volcanic network at and near the Boku Volcanic Complex (Boku VC). Two-dimensional gravity models and an upward continuation map analysis of the upper crust reveal a gravity maximum that is interpreted as mafic intrusion at depths between 5 and 10 km beneath the Boku VC. A circular gravity maximum on the upward continued and residual gravity anomaly maps over the Boku VC and adjacent segments suggest the shallow plumbing systems beneath the segments are discrete, but that they merge into the deeper crust. The gravity models suggest that below 5 km beneath the center of magmatic segments nearly all the extension over the last 2 My can be accounted for by magmatic intrusion. Our models require faults in the uppermost crust which likely contribute to extension and may serve locally as conduits for the conveying melts or hydrothermal fluids. Our gravity analysis supports petrological studies that indicate a two-level magmatic plumbing system beneath the Wonji fault belts in which a melt supply from the upper mantle moves to mid-crust and then to shallow upper crust where the magma fractionates into more siliceous magma within smaller magma chambers.

General solution for linear 2D anisotropic surface gravity water waves on uniform current

Measuring and modeling ocean waves is a routine task for oceanographers and marine engineers. Accounting for current effects on waves is less common; however, such effects can be non-trivial, particularly for strong currents. Recent research has also found that currents are increasing with global temperatures. Thus, accounting for currents is of potential importance to a growing subset of real-world environments. One significant impact of currents is their modification of dispersion. It is known that, in contrast to dispersion without current, wave–current dispersion is multivalued and anisotropic, meaning it varies with direction and can yield multiple solutions for the same frequency. Strictly speaking, a complete analysis ought to account for all dispersion solutions. This study presents a general wave field solution for linear steady-state two-dimensional surface gravity waves on current. In contrast to existing formulations, it accounts for the complete set of dispersion solutions. The multiple solutions correspond to linearly independent (same frequency) spatial modes with no analogy in models without current. To fully determine the complete temporal and spatial features of a wave field, one must determine the amplitudes of all spatial modes. This can be achieved through the solution of an inverse problem, provided one has sufficient initial conditions. The significance of accounting for all spatial modes is demonstrated through examples. It is shown that a single time-series measurement is insufficient for determining the spatial features of a monochromatic (single frequency) wave. Rather, additional spatial information must be introduced to render the problem well-posed. The theory and methodology presented can be used to improve wave models and measurements.

Black hole wavefunctions and microcanonical states

We consider the problem of defining a microcanonical thermofield double state at fixed energy and angular momentum from the gravitational path integral. A semiclassical approximation to this state is obtained by imposing a mixed boundary condition on an initial time surface. We analyze the corresponding boundary value problem and gravitational action. The overlap of this state with the canonical thermofield double state, which is interpreted as the Hartle-Hawking wavefunction of an eternal black hole in a mini-superspace approximation, is calculated semiclassically. The relevant saddlepoint is a higher-dimensional, rotating generalization of the wedge geometry that has been studied in two-dimensional gravity. Along the way we discuss a new corner term in the gravitational action that arises at a rotating horizon.

Fully screened two-dimensional magnetoplasmons and rotational gravity shallow water waves in a rectangle

Fully screened two-dimensional magnetoplasmons and rotational gravity shallow water waves in a rectangle

Gravitating kinks with asymptotically flat metrics

In this work, we consider a two-dimensional (2D) dilaton gravity model where the dilaton kinetic term is modified by an additional derivative coupling term . In the case with a canonical scalar matter field, the field equations of this model have a simple first-order formalism, from which exact static kink solutions can be constructed. The novelty of these solutions is that the corresponding metric can be asymptotically flat rather than asymptotically anti-de Sitter. The linear stability and the localization of scalar matter fields are also studied. It was found that the solutions are stable against small linear perturbations, and the localization of scalar matter fields can be realized by introducing scalar-kink interactions.

Some Generalizations of Mirzakhani's Recursion and Masur-Veech Volumes via Topological Recursions

Via Andersen-Borot-Orantin's geometric recursion, a twist of the topological recursion was proposed, and a recursion for the Masur-Veech polynomials was uncovered. The purpose of this article is to explore generalizations of Mirzakhani's recursion based on physical two-dimensional gravity models related to the Jackiw-Teitelboim gravity and to provide an introduction to various realizations of topological recursion. For generalized Mirzakhani's recursions involving a Masur-Veech type twist, we derive Virasoro constraints and cut-and-join equations, and also show some computations of generalized volumes for the physical two-dimensional gravity models.

From minimal strings towards Jackiw–Teitelboim gravity: on their resurgence, resonance, and black holes

Abstract Two remarkable facts about Jackiw–Teitelboim (JT) two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensembles are described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e. changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series). These analyses are first done via spectral geometry, at both perturbative and nonperturbative levels, addressing the resurgent large-order growth of perturbation theory, alongside a calculation of nonperturbative instanton-actions and corresponding Stokes data. This calculation requires an algorithm to reach large-order, which is valid for arbitrary two-dimensional topological gravity. String equations—as derived from the Gel’fand–Dikii construction of the resolvent—are analyzed in both multicritical and minimal string theoretic contexts, and studied both perturbatively and nonperturbatively (always matching against the earlier spectral-geometry computations). The resulting solutions, as described by resurgent transseries, are shown to be resonant. The large matter-central-charge limit is addressed—in the string-equation context—and, in particular, the string equation for JT gravity is obtained to next derivative-orders, beyond the known genus-zero case (its possible exact-form is also discussed). Finally, a discussion of gravitational perturbations to Schwarzschild-like black hole solutions in these minimal-string models, regarded as deformations of JT gravity, is included—alongside a brief discussion of quasinormal modes.

Dimensional reduction of the S3/WZW duality

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Linear Time-Invariant Models of a Large Cumulus Ensemble

Abstract Methods in system identification are used to obtain linear time-invariant state-space models that describe how horizontal averages of temperature and humidity of a large cumulus ensemble evolve with time under small forcing. The cumulus ensemble studied here is simulated with cloud-system-resolving models in radiative–convective equilibrium. The identified models extend steady-state linear response functions used in past studies and provide accurate descriptions of the transfer function, the noise model, and the behavior of cumulus convection when coupled with two-dimensional gravity waves. A novel procedure is developed to convert the state-space models into an interpretable form, which is used to elucidate and quantify memory in cumulus convection. The linear problem studied here serves as a useful reference point for more general efforts to obtain data-driven and interpretable parameterizations of cumulus convection.

Kink solutions in generalized 2D dilaton gravity

We study static kink solutions in a generalized two-dimensional dilaton gravity model, where the kinetic term of the dilaton is generalized to be an arbitrary function of the canonical one X=−12(∇φ)2, say F(X), and the kink is generated by a canonical scalar matter field ϕ. It is found that for arbitrary F(X), the background field equations have a simple first-order formalism, and the linear perturbation equation can always be written as a Schrödinger-like equation with factorizable Hamiltonian operator. After choosing appropriate F(X) and superpotential, we obtain a sine-Gordon type kink solution with pure AdS2 metric. The linear perturbation issue of this solution becomes an exactly solvable conformal quantum mechanics problem, if one of the model parameter takes a critical value.

Investigation into a deep-rooted crustal framework deduced from potential field data in Cretaceous and Tertiary strata, Sokoto Basin NW, Nigeria

The Paleocene sediments from the Sokoto Group, which comprises of the Gamba, Dange, and Kalambaina formations, were covered by Maastrichtian sediments from the Rima Group, which includes the Wurno, Dukamaje, and Taloka formations. High-resolution aeromagnetic and satellite gravity measurements were used to study these sediments. The aforementioned strata correspond to the Cretaceous and Tertiary strata in this research area and are situated in the south-eastern part of the Iullemmeden Basin. Our aim is to determine and explain the horizontal variation in density and magnetization using the whole regional satellite gravity and aeromagnetic data. The deeper magnetic and density sources were scanned using a two-dimensional (2D) radially averaged power spectrum analysis to produce the NE to SW and E to W trending models for the Moho, lower, and upper lithosphere under the study area. The results were further assessed using upward continuation, derivative analysis, and two-dimensional gravity and magnetic modeling. Numerous important structural trends (i.e., NE-SW, E-W & ENE-WSW), have been identified as a result of the vertical gradients for the potential field data. Spectral analysis and Euler deconvolution can be used to calculate the depths to the lower and upper mantle crust boundaries as well as the depth to Moho. The findings of a qualitative analysis point to an intrusion of the Gundumi and Illo Formations that has a northeast orientation as the primary cause of the significant gravitational and magnetic interaction. The differences in the deep-seated crustal structures and mineralized anomalous bodies with depth were visible on anomaly maps with an upward continuation of 5 km, 7 km, 20 km, and 30 km. Quantitatively, the 2D regional models along the selected profiles (L1, L2, L4, L6 and L7) display a typical lithostratigraphic succession of the Gundumi and Illo Formation (Continental Intercalaire, CI) type of crust, which is subdivided into the lower and upper mantle crust as well as the Moho. The sediment thickness by surface depth ranges from ∼4.06 km and ∼23.31 km. The Moho interface, lower and upper mantle crusts, and magnetic crust are all located at depths of around ∼10.23 km. The distance between the local models of the foundation rocks to the north and south of the Sokoto Group was approximately ∼6 to ∼8 km and ∼4.5 km, respectively.

Gravitational action for a massive Majorana fermion in 2d quantum gravity

We compute the gravitational action of a free massive Majorana fermion coupled to two-dimensional gravity on compact Riemann surfaces of arbitrary genus. The structure is similar to the case of the massive scalar. The small-mass expansion of the gravitational yields the Liouville action at zeroth order, and we can identify the Mabuchi action at first order. While the massive Majorana action is a conformal deformation of the massless Majorana CFT, we find an action different from the one given by the David-Distler-Kawai (DDK) ansatz.

Posterior analysis of particle swarm optimization results applied to gravity inversion in sedimentary basins

<abstract><p>As is well known, it is impossible to model reality with its true level of detail. Additionally, it is impossible to make an infinite number of observations, which are always contaminated by noise. These circumstances imply that, in an inverse problem, the misfit of the best estimated model will always be less than that of the true one. Therefore, it is not possible to reconstruct the model that actually generated the collected observations. The best way to express the solution of an inverse problem is as a collection of models that explain the observations at a certain misfit level according to a defined cost function. One of the main advantages of global search methods over local ones is that, in addition to not depending on an initial model, they provide a set of generated models with which statistics can be made. In this paper we present a technique for analyzing the results of any global search method, particularized to the particle swarm optimization algorithm applied to the solution of a two-dimensional gravity inverse problem in sedimentary basins. Starting with the set of generated models, we build the equivalence region of a predefined tolerance which contains the best estimated model, i.e., which involves the estimated global minimum of the cost function. The presented algorithm improves the efficiency of the equivalence region detection compared to our previous works.</p></abstract>

The discreet charm of the discrete series in dS2

We study quantum field theories placed on a two-dimensional de Sitter spacetime (dS2) with an eye on the group-theoretic organization of single and multi-particle states. We explore the distinguished role of the discrete series unitary irreducible representation (UIR) in the Hilbert space. By employing previous attempts to realize these states in free tachyonic scalar field theories, we propose how the discrete series may contribute to the Källén–Lehmann decomposition of an interacting scalar two-point function. We also study BF gauge theories with SL(N,R) gauge group in dS2 and establish a relation between the discrete series UIRs and the operator content of these theories. Although present at the level of the operators, states carrying discrete series quantum numbers are projected out of the gauge-invariant Hilbert space. This projection is reminiscent of what happens for quantum field theories coupled to semiclassical de Sitter gravity, where we must project onto the subspace of de Sitter invariant states. We discuss how to impose the diffeomorphism constraints on local field-theory operators coupled to two-dimensional gravity in de Sitter, with particular emphasis on the role of contact terms. Finally, we discuss an SYK-type model with a random two-body interaction that encodes an infinite tower of discrete series operators. We speculate on its potential microscopic connection to the SL(N,R) BF theory in the large-N limit.

Supersymmetric localization of (higher-spin) JT gravity: a bulk perspective

We study two-dimensional Jackiw-Teitelboim gravity on the disk topology by using a BF gauge theory in the presence of a boundary term. The system can be equivalently written in a supersymmetric way by introducing auxiliary gauginos and scalars with suitable boundary conditions on the hemisphere. We compute the exact partition function thanks to supersymmetric localization and we recover the result obtained from the Schwarzian theory by accurately identifying the physical scales. The calculation is then easily extended to the higher-spin generalization of Jackiw-Teitelboim gravity, finding perfect agreement with previous results. We argue that our procedure can also be applied to boundary-anchored Wilson lines correlators.

Dispersion effects in porous medium gravity currents experiencing local drainage

We develop a theoretical model to study (dense) two-dimensional gravity current flow in a laterally extensive porous medium experiencing leakage through a discrete fissure situated along this boundary at some finite distance from the injection point. Our model, which derives from the depth-averaged mass and buoyancy equations in conjunction with Darcy's law, considers dispersive mixing between the gravity current and the surrounding ambient by allowing two different gravity current phases. Thus do we define a bulk phase consisting of fluid whose density is close to that of the source fluid and a dispersed phase consisting of fluid whose density is close to that of the ambient. We characterize the degree of dispersion by estimating, as a function of time, the buoyancy of the dispersed phase and the separation distance between the bulk nose and the dispersed nose. On this basis, it can be shown that the amount of dispersion depends on the flow conditions upstream of the fissure, the fissure permeability and the vertical and horizontal extents of the fissure. We also show that dispersion is larger when the gravity current propagates along an inclined barrier rather than along a horizontal barrier. Model predictions are fitted against numerical simulations. The simulations in question are performed using COMSOL and consider different inclination angles and fissure and upstream flow conditions. Our study is motivated by processes related to underground $\mathrm {H}_2$ storage e.g. an irrecoverable loss of $\mathrm {H}_2$ when it is injected into the cushion gas saturating an otherwise depleted natural gas reservoir.