arXiv subjects

Damián A. Galante

Publications and source records attributed to Damián A. Galante.

At least 19 recordsLinked to original sources

arXiv2026

Conformal boundaries near extremal black holes

We examine four dimensional, near-extremal black hole solutions in the presence of a finite boundary obeying conformal boundary conditions, where the conformal class of the induced metric and the trace of the extrinsic curvature are fixed. Working in Euclidean signature and at fixed charge, we find the near-extremal regime is dominated by a double-scaling limit which reveals new scaling laws for the quasi-local conformal entropy at low temperatures. Upon spherical dimensional reduction, we obtain the effective two-dimensional dilaton-gravity theory that describes the near-extremal regime. In contrast to Dirichlet boundaries, for conformal boundaries a linear dilaton potential is not sufficient to capture the leading correction away from extremality and higher orders are needed. We also examine near-Nariai solutions and the spherical reduction of pure three-dimensional gravity in (Anti-) de Sitter space. In the latter, provided the boundary is placed near the conformal boundary of three-dimensional Anti-de Sitter space, the dynamics of the spherically symmetric boundary mode is governed by a Liouville equation that descends from a (minus) Schwarzian effective action.

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arXiv2026

Conformal Boundary Conditions and Higher Curvature Gravity

We initiate a systematic study of Einstein-Gauss-Bonnet gravity in the presence of boundaries subject to conformal boundary conditions, in which the conformal class of the boundary metric is kept fixed. In Einstein gravity, the trace of the extrinsic curvature is also fixed at the boundary. Here we generalize this boundary condition with the appropriate higher curvature correction. We study the problem both in Euclidean and Lorentzian signature. In Euclidean signature, we show that, similarly to the Einstein gravity case, the entropy at large temperatures exhibits the behavior of a conformal field theory in one lower dimension. We also show that in the flat space limit, the higher curvature corrections do not contribute to the leading behavior at high temperatures. We conjecture that this result is a universal feature of the flat space limit in the presence of conformal boundaries. We test our conjecture by analyzing charged black holes. In Lorentzian signature, we analyze the dynamics of the boundary Weyl factor in black hole backgrounds at the linearized level.

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arXiv2026

The Stretched Horizon Limit

We consider four-dimensional general relativity with a positive cosmological constant, $Λ$, in the presence of a boundary, $Γ$, of finite spatial size. The boundary is located near a cosmological event horizon, and is subject to boundary conditions that fix the conformal class of the induced metric, and, $K$, the trace of the extrinsic curvature along $Γ$. The proximity of $Γ$ to the horizon is controlled by the dimensionless parameter ${K}{Λ^{-\frac{1}{2}}}$. We provide an exhaustive analysis of linearised gravitational perturbations for the setup. This is performed both for a $Γ$ encasing a portion of the static patch that ends just before the cosmological horizon (pole patch), as well as a $Γ$ containing only the region near the cosmological horizon (cosmic patch). In the pole patch, we uncover a layered hierarchy of modes: ordinary normal modes, a novel type of boundary gapless mode, and boundary soft modes of frequency $ω\approx \pm 2πi T_{\text{dS}}$, with $T_{\text{dS}}$ the horizon temperature. Minkowskian behaviour is recovered only for angular momenta $l \gtrsim {K}{Λ^{-\frac{1}{2}}}$ which can be made parametrically large, thus attenuating previously found growing modes. In the cosmic patch, we uncover sound and shear fluid-dynamical modes that we interpret in terms of a conformal fluid with shear viscosity over entropy density ratio $\tfracη{s} = \tfrac{1}{4π}$ and vanishing bulk viscosity $ζ=0$. The fluid dynamical sector is shown to admit a non-linear treatment. We describe a scaling regime in which the stretched horizon gravitational dynamics is dictated by a universal Rindler geometry, independent to the details of the infilling horizon. We briefly discuss quantitative features that distinguish cosmological and black hole horizons away from the Rindler regime.

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arXiv2026

Exploring the Infrared Landscape of the SYK Model

We analyse a class of SYK models whose Hamiltonian is the sum of two SYK Hamiltonians with different numbers of fermions $q, \tilde q$ in each interaction. We consider both Euclidean and Lorentzian probes of the quantum system in the large $N$ limit. In the strong coupling phase, the entropy provides a diagnostic of the thermal renormalisation group flow. Under certain conditions, two parametrically separated regimes of near-conformal behaviour emerge. The first reproduces the standard linear-in-temperature scaling characteristic of the single SYK model. The system then flows to another near-fixed point whose entropy scaling depends on the ratio $n = q/\tilde q$. For $n<3/2$, the entropy exhibits anomalous, stronger-than-linear scaling in temperature. At $n=3/2$, there is an additional logarithmic enhancement. Using conformal perturbation theory, we argue that in the infrared regime of the SYK model, there may exist disordered conformal operators with dimensions $1 < Δ\leq 3/2$. In Lorentzian signature, we study the out-of-time-ordered correlator and show that these deformed theories exhibit near-maximal chaos in both regimes (when they exist). We comment on the relation between the anomalous scalings found here and those observed in certain near-extremal black holes in two and higher dimensions.

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arXiv2025

Gravitational Observatories

We consider four-dimensional general relativity with vanishing cosmological constant defined on a manifold with a boundary. In Lorentzian signature, the timelike boundary is of the form $\boldsymbolσ \times \mathbb{R}$, with $\boldsymbolσ$ a spatial two-manifold that we take to be either flat or $S^2$. In Euclidean signature, we take the boundary to be $S^2\times S^1$. We consider conformal boundary conditions, whereby the conformal class of the induced metric and trace $K$ of the extrinsic curvature are fixed at the timelike boundary. The problem of linearised gravity is analysed using the Kodama-Ishibashi formalism. It is shown that for a round metric on $S^2$ with constant $K$, there are modes that grow exponentially in time. We discuss a method to control the growing modes by varying $K$. The growing modes are absent for a conformally flat induced metric on the timelike boundary. We provide evidence that the Dirichlet problem for a spherical boundary does not suffer from non-uniqueness issues at the linearised level. We consider the extension of black hole thermodynamics to the case of conformal boundary conditions, and show that the form of the Bekenstein-Hawking entropy is retained.

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arXiv2025

Gravitational Observatories in AdS$_4$

We consider four-dimensional general relativity with a negative cosmological constant in the presence of a finite size boundary, $Γ$, for both Euclidean and Lorentzian signature. As our boundary condition, we consider the `conformal' boundary condition that fixes the conformal class of the induced metric at $Γ$ and the trace of the extrinsic curvature, $K(x^m)$. In Lorentzian signature, we must supplement these with appropriate initial data comprising the standard Cauchy data along a spatial slice and, in addition, initial data for a boundary mode that appears due to the presence of the finite size boundary. We perform a linearised analysis of the gravitational field equations for both an $S^2\times \mathbb{R}$ as well as a Minkowskian, $\mathbb{R}^{1,2}$, boundary. In the $S^2\times \mathbb{R}$ case, in addition to the usual AdS$_4$ normal modes, we uncover a novel linearised perturbation, $\boldsymbolω(x^m)$, which can exhibit complex frequencies at sufficiently large angular momentum. Upon moving $Γ$ toward the infinite asymptotic AdS$_4$ boundary, the complex frequencies appear at increasingly large angular momentum and vanish altogether in the strict limit. In the $\mathbb{R}^{2,1}$ case, although we uncover an analogous novel perturbation, we show it does not exhibit complex frequencies. In Euclidean signature, we show that $K(x^m)$ plays the role of a source for $\boldsymbolω(x^m)$. When close to the AdS$_4$ asymptotic boundary, we speculate on the holographic interpretation of $\boldsymbolω(x^m)$.

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arXiv2025

Cosmological Observatories

We study the static patch of de Sitter space in the presence of a timelike boundary. We impose that the conformal class of the induced metric and the trace of the extrinsic curvature, $K$, are fixed at the boundary. We present the thermodynamic structure of de Sitter space subject to these boundary conditions, for static and spherically symmetric configurations to leading order in the semiclassical approximation. In three spacetime dimensions, and taking $K$ constant on a toroidal Euclidean boundary, we find that the spacetime is thermally stable for all $K$. In four spacetime dimensions, the thermal stability depends on the value of $K$. It is established that for sufficiently large $K$, the de Sitter static patch subject to conformal boundary conditions is thermally stable. This contrasts the Dirichlet problem for which the region encompassing the cosmological horizon has negative specific heat. We present an analysis of the linearised Einstein equations subject to conformal boundary conditions. In the worldline limit of the timelike boundary, the underlying modes are linked to the quasinormal modes of the static patch. In the limit where the timelike boundary approaches the cosmological event horizon, the linearised modes are interpreted in terms of the shear and sound modes of a fluid dynamical system. Additionally, we find modes with a frequency of positive imaginary part. Measured in a local inertial reference frame, and taking the stretched cosmological horizon limit, these modes grow at most polynomially.

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arXiv2024

Krylov complexity and chaos in deformed SYK models

Krylov complexity has recently been proposed as a quantum probe of chaos. The Krylov exponent characterising the exponential growth of Krylov complexity is conjectured to upper-bound the Lyapunov exponent. We compute the Krylov and the Lyapunov exponents in the Sachdev-Ye-Kitaev model and in some of its deformations. We do this analysis both at infinite and finite temperatures, in models where the number of fermionic interactions is both finite and infinite. We consider deformations that interpolate between two regions of near-maximal chaos and deformations that become nearly-integrable at low temperatures. In all cases, we find that the Krylov exponent upper-bounds the Lyapunov one. However, we find that while the Lyapunov exponent can have non-monotonic behaviour as a function of temperature, in all studied examples the Krylov exponent behaves monotonically. For instance, we find models where the Lyapunov exponent goes to zero at low temperatures, while the Krylov exponent saturates to its maximal bound. We speculate on the possibility that this monotonicity might be a generic feature of the Krylov exponent in quantum systems evolving under unitary evolution.

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arXiv2023

Renormalisation Group Flows of Deformed SYK Models

We explore computationally tractable deformations of the SYK model. The deformed theories are described by the sum of two SYK Hamiltonians with differing numbers, $q$ and $\tilde{q}$, of interacting fermions. In the large $N$ limit, employing analytic and numerical tools, we compute finite temperature correlation functions and thermodynamic quantities. We identify a novel analytically solvable model in the large $q$ limit. We find that, under certain circumstances, the thermal RG flow in the strongly coupled infrared phase exhibits two regions of linear-in-temperature entropy, which we interpret in terms of Schwarzian actions. Using conformal perturbation theory we compute the leading relevant correction away from the intermediate near-conformal fixed point. Holographic spacetimes in two spacetime dimensions that reproduce the thermodynamics of the microphysical theory are discussed. These are flow geometries that interpolate between two Euclidean near-AdS$_2$ spacetimes with different radii. The Schwarzian soft mode corresponding to the AdS$_2$ region in the deep interior resides entirely within the geometric regime.

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arXiv2023

Complex geodesics in de Sitter space

The two-point function of a free massive scalar field on a fixed background can be evaluated in the large mass limit by using a semiclassical geodesic approximation. In de Sitter space, however, this poses a puzzle. Certain spacelike separated points are not connected by real geodesics despite the corresponding two-point function in the Bunch-Davies state being non-vanishing. We resolve this puzzle by considering complex geodesics after analytically continuing to the sphere. We compute one-loop corrections to the correlator and discuss the implications of our results to de Sitter holography.

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arXiv2023

Finite Features of Quantum De Sitter Space

We consider degrees of freedom for a quantum de Sitter spacetime. The problem is studied from both a Lorentzian and a Euclidean perspective. From a Lorentzian perspective, we compute dynamical properties of the static patch de Sitter horizon. These are compared to dynamical features of black holes. We point out differences suggestive of non-standard thermal behaviour for the de Sitter horizon. We establish that geometries interpolating between an asymptotically AdS$_2 \times S^2$ space and a dS$_4$ interior are compatible with the null energy condition, albeit with a non-standard decreasing radial size of $S^2$. The putative holographic dual of an asymptotic AdS$_2$ spacetime is comprised of a finite number of degrees of freedom. From a Euclidean perspective we consider the gravitational path integral for fields over compact manifolds. In two-dimensions, we review Polchinski's BRST localisation of Liouville theory and propose a supersymmetric extension of timelike Liouville theory which exhibits supersymmetric localisation. We speculate that localisation of the Euclidean gravitational path integral is a reflection of a finite number of degrees of freedom in a quantum de Sitter universe.

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arXiv2022

Shape Deformations of Charged Rényi Entropies from Holography

Charged and symmetry-resolved Rényi entropies are entanglement measures quantifying the degree of entanglement within different charge sectors of a theory with a conserved global charge. We use holography to determine the dependence of charged Rényi entropies on small shape deformations away from a spherical or planar entangling surface in general dimensions. This dependence is completely characterized by a single coefficient appearing in the two point function of the displacement operator associated with the Rényi defect. We extract this coefficient using its relation to the one point function of the stress tensor in the presence of a deformed entangling surface. This is mapped to a holographic calculation in the background of a deformed charged black hole with hyperbolic horizon. We obtain numerical solutions for different values of the chemical potential and replica number $n$ in various spacetime dimensions, as well as analytic expressions for small chemical potential near $n=1$. When the Rényi defect becomes supersymmetric, we demonstrate a conjectured relation between the two point function of the displacement operator and the conformal weight of the twist operator.

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arXiv2021

Holographic Complexity and de Sitter Space

We compute the length of spacelike geodesics anchored at opposite sides of certain double-sided flow geometries in two dimensions. These geometries are asymptotically anti-de Sitter but they admit either a de Sitter or a black hole event horizon in the interior. While in the geometries with black hole horizons, the geodesic length always exhibit linear growth at late times, in the flow geometries with de Sitter horizons, geodesics with finite length only exist for short times of the order of the inverse temperature and they do not exhibit linear growth. We comment on the implications of these results towards understanding the holographic proposal for quantum complexity and the holographic nature of the de Sitter horizon.

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arXiv2020

Constructing AdS_2 flow geometries

We consider two-dimensional geometries flowing away from an asymptotically AdS$_2$ spacetime. Macroscopically, flow geometries and their thermodynamic properties are studied from the perspective of dilaton-gravity models. We present a precise map constructing the fixed background metric from the boundary two-point function of a nearly massless matter field. We analyse constraints on flow geometries, viewed as solutions of dimensionally reduced theories, stemming from energy conditions. Microscopically, we construct computationally tractable RG flows in SYK-type models at vanishing and non-vanishing temperature. For certain regimes of parameter space, the flow geometry holographically encoding the microscopic RG flow is argued to interpolate between two (near) AdS$_2$ spacetimes. The coupling between matter fields and the dilaton in the putative bulk is also discussed. We speculate on microscopic flows interpolating between an asymptotically AdS$_2$ spacetime and a portion of a dS$_2$ world.

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arXiv2020

De Sitter Horizons & Holographic Liquids

We explore asymptotically AdS$_2$ solutions of a particular two-dimensional dilaton-gravity theory. In the deep interior, these solutions flow to the cosmological horizon of dS$_2$. We calculate various matter perturbations at the linearised and non-linear level. We consider both Euclidean and Lorentzian perturbations. The results can be used to characterise the features of a putative dual quantum mechanics. The chaotic nature of the de Sitter horizon is assessed through the soft mode action at the AdS$_2$ boundary, as well as the behaviour of shockwave type solutions.

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arXiv2020

Traversable wormholes in AdS and bounds on information transfer

We analyze the amount of information that can be sent through the traversable wormholes of Gao, Jafferis, and Wall. Although we find that the wormhole is open for a proper time shorter than the Planck time, the transmission of a signal through the wormhole can sometimes remain within the semiclassical regime. For black holes with horizons of order the AdS radius, information cannot be reliably sent through the wormhole. However, black holes with horizon radius much larger than the AdS radius do allow for the transmission of a number of quanta of order the horizon area in AdS units. More information can be sent through the wormhole by increasing the number of light fields contributing to the negative energy. Our bulk computations agree with a boundary analysis based on quantum teleportation.

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arXiv2017

Universality in fast quantum quenches

We expand on the investigation of the universal scaling properties in the early time behaviour of fast but smooth quantum quenches in a general $d$-dimensional conformal field theory deformed by a relevant operator of dimension $Δ$ with a time-dependent coupling. The quench consists of changing the coupling from an initial constant value $λ_1$ by an amount of the order of $δλ$ to some other final value $λ_2$, over a time scale $δt$. In the fast quench limit where $δt$ is smaller than all other length scales in the problem, $ δt \ll λ_1^{1/(Δ-d)}, λ_2^{1/(Δ-d)}, δλ^{1/(Δ-d)}$, the energy (density) injected into the system scales as $δ{\cal E} \sim (δλ)^2 (δt)^{d-2Δ}$. Similarly, the change in the expectation value of the quenched operator at times earlier than the endpoint of the quench scales as $<{\cal O}_Δ> \sim δλ(δt)^{d-2Δ}$, with further logarithmic enhancements in certain cases. While these results were first found in holographic studies, we recently demonstrated that precisely the same scaling appears in fast mass quenches of free scalar and free fermionic field theories. As we describe in detail, the universal scaling refers to renormalized quantities, in which the UV divergent pieces are consistently renormalized away by subtracting counterterms derived with an adiabatic expansion. We argue that this scaling law is a property of the conformal field theory at the UV fixed point, valid for arbitrary relevant deformations and insensitive to the details of the quench protocol. Our results highlight the difference between smooth fast quenches and instantaneous quenches where the Hamiltonian abruptly changes at some time.

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arXiv2017

An exactly solvable quench protocol for integrable spin models

Quantum quenches in continuum field theory across critical points are known to display different scaling behaviours in different regimes of the quench rate. We extend these results to integrable lattice models such as the transverse field Ising model on a one-dimensional chain and the Kitaev model on a two-dimensional honeycomb lattice using a nonlinear quench protocol which allows for exact analytical solutions of the dynamics. Our quench protocol starts with a finite mass gap at early times and crosses a critical point or a critical region, and we study the behaviour of one point functions of the quenched operator at the critical point or in the critical region as a function of the quench rate. For quench rates slow compared to the initial mass gap, we find the expected Kibble-Zurek scaling. In contrast, for rates fast compared to the mass gap, but slow compared to the inverse lattice spacing, we find scaling behaviour similar to smooth fast continuum quenches. For quench rates of the same order of the lattice scale, the one point function saturates as a function of the rate, approaching the results of an abrupt quench. The presence of an extended critical surface in the Kitaev model leads to a variety of scaling exponents depending on the starting point and on the time where the operator is measured. We discuss the role of the amplitude of the quench in determining the extent of the slow (Kibble-Zurek) and fast quench regimes, and the onset of the saturation.

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