arXiv subjects

Shao-Feng Wu

Publications and source records attributed to Shao-Feng Wu.

At least 19 recordsLinked to original sources

arXiv2026

Metric Reconstruction from Timelike Entanglement Entropy

Timelike entanglement entropy (TEE) provides a Lorentzian boundary probe of bulk geometry, but its use for metric reconstruction depends on the holographic prescription and on the extremal-surface branch selected by that prescription. We study this inverse problem for strip-shaped TEE data and make these dependencies explicit. In the complex-valued weak extremal surface (CWES) prescription, the time-width dependence of TEE determines an Abel density $H(W)$ on a selected real branch; for Bañados-Teitelboim-Zanelli (BTZ) black holes this gives an analytic reconstruction of the blackening factor once the singularity endpoint fixes the radial origin. After developing a forward numerical method for the complex-coordinate prescription, we formulate it as the main reconstruction scheme for the asymptotically $AdS_{d+1}$ backgrounds with $d\geq 2$. On a chosen complex branch, the time-width dependence of TEE supplies the Abel input that determines the TEE-accessible density, while one additional geometric anchor is required to convert that density into a definite radial metric profile. With UV or horizon-scale anchoring and rational continuation from the reconstructed complex-path samples, the method reproduces the benchmark BTZ, four-dimensional Schwarzschild, and Reissner-Nordström (RN) blackening factors. However, the Gubser-Rocha example shows that a single strip observable with a nontrivial spatial warp factor determines only one functional combination of the metric functions.

hep-th↗

arXiv2026

Holographic Learning from Fermionic Spectra: Application to Strange Metal Phenomenology

We develop a data-driven framework based on Neural ODEs that learns the effective bulk metric functions and the charge-weighted gauge potential $qA_t$ of a static, planar-symmetric black hole from boundary fermionic spectral functions. After validating the framework on the Einstein--Maxwell and Gubser--Rocha models with high accuracy, we apply it to the nodal strange-metal phenomenology of the cuprate $\mathrm{(Pb,Bi)_2Sr_{2-x}La_xCuO_{6+δ}}$ within a semi-holographic setting, taking as input the normalized target generated from the extended power-law liquid (PLL) model calibrated by angle-resolved photoemission measurements. A key structural observation is that our probe fermion is massless and therefore insensitive to the conformal factor, leading to a coordinate/Weyl redundancy, while spectral normalization introduces a degeneracy in the scaled Hawking temperature. After identifying these sources of nonuniqueness, we find that, at low temperatures and near-optimal doping, the normalized extended-PLL target can be well described by a family of effective geometries close to the conformal-to-$\mathrm{AdS}_{2}\times\mathbb{R}^{2}$ black-hole class, with a nearly vanishing $qA_t$ ($\sim10^{-4}\,\mathrm{eV}$). The conformal-factor ambiguity further implies that fixing macroscopic thermodynamics such as the electronic specific heat requires independent input beyond the fermionic spectra. We also examine the applicability of our framework across doping and temperature: at low temperatures, the learned effective model remains viable throughout the studied doping range, with only a mild increase in loss toward the overdoped side; at higher temperatures, however, both the loss and $qA_t$ increase substantially.

hep-th↗

arXiv2026

Probing bulk geometry via pole skipping: from static to rotating spacetimes

We investigate an analytical framework for reconstructing bulk geometries from pole-skipping data. Previously, this method enabled the recursive recovery of near-horizon metric derivatives in static, planar-symmetric black holes. Building on this framework, we systematically extend it to more intricate geometries, specifically static topological black holes and rotating black holes. For three-dimensional rotating black holes, we demonstrate that the metric can be fully reconstructed from boundary pole-skipping data. For four-dimensional rotating spacetimes admitting a separable coordinate system (such as the Kerr family), standard near-horizon pole-skipping successfully reconstructs the purely radial metric functions. To recover the remaining angular metric functions, we introduce a mathematical counterpart termed "angular pole-skipping," defined via a near-axis analysis. Although its precise holographic dictionary remains an open question, this bulk-side formalism completes the geometric reconstruction algorithm. Furthermore, we demonstrate that the vacuum Einstein equations can be recast as a set of algebraic equations governing the pole-skipping data and that the null energy condition imposes algebraic inequalities on this boundary data. Finally, we establish general polynomial constraints dictated by the overdetermined nature of the metric reconstruction, highlighting the highly redundant encoding of bulk geometry in boundary data.

gr-qc↗

arXiv2026

Emergence of Time Semicrystals in Holographic Driven-Dissipative Systems

Understanding how temporal order degrades in quantum systems remains a central issue in nonequilibrium physics. Here we study the melting of discrete time crystals in a periodically driven holographic system, where a distinct (discrete) time semicrystal phase emerges with persistent temporal order in disorder, bridging discrete time crystals and fully disordered regimes. This phase exhibits a periodic skeleton, with discrete subharmonic peaks persisting atop a continuous spectrum. We extract a critical scaling behavior across the discrete time crystal to time semicrystal transition. Furthermore, even dynamical transitions between distinct periodic skeletons can be clearly identified with systematic log-periodic corrections to power-law scaling, revealing discrete scale invariance. These findings in holography significantly enrich the platforms for studying nonequilibrium phases of matter.

hep-th↗

arXiv2025

Learning geometries beyond asymptotic AdS

We present a data-driven method for holographic bulk reconstruction that works even when the spacetime is not asymptotically AdS. Given the data of boundary Green functions within a finite frequency window, we iteratively adjust a bulk metric with a finite radial cutoff until its holographic Green functions reproduce the boundary data. Based on the holographic Wilsonian renormalization group for the Klein-Gordon equation in an undetermined curve space, we construct a radial flow equation and transform it into a Neural ODE, which is an infinite-depth neural network for modeling continuous dynamics. Assuming the double-trace coupling $h$ in the Wilsonian action is real, we demonstrate that the Neural ODE can effectively learn the metrics with AdS, Lifshitz, and hyperscaling violated asymptotics. In particular, we apply the algorithm to the Sachdev-Ye-Kitaev (SYK) model which slightly deviates from the conformal limit. In the hyperparameter space spanned by the rescaled temperature $\bar{T}$ and the radial cutoff $ε$, we identify a critical curve along which the learned metric is close to AdS$_2$ black hole with finite cutoff. We derive an approximate analytical expression for this curve, from which an effective bulk dual of the SYK coupling $v$ is established. Our work provides a promising way for using machine learning to depict the novel bulk geometry dual to the non-conformal boundary systems in the real world.

hep-th↗

arXiv2025

Discover physical concepts and equations with machine learning

Machine learning can uncover physical concepts or physical equations when prior knowledge from the other is available. However, these two aspects are often intertwined and cannot be discovered independently. We extend SciNet, which is a neural network architecture that simulates the human physical reasoning process for physics discovery, by proposing a model that combines Variational Autoencoders (VAE) with Neural Ordinary Differential Equations (Neural ODEs). This allows us to simultaneously discover physical concepts and governing equations from simulated experimental data across various physical systems. We apply the model to several examples inspired by the history of physics, including Copernicus' heliocentrism, Newton's law of gravity, Schrödinger's wave mechanics, and Pauli's spin-magnetic formulation. The results demonstrate that the correct physical theories can emerge in the neural network.

cs.LG↗

arXiv2024

Neural ODEs for holographic transport models without translation symmetry

We investigate the data-driven holographic transport models without translation symmetry, focusing on the real part of frequency-dependent shear viscosity, $η_{\mathrm{re}}(ω)$. We develop a radial flow equation of the shear response and establish its relation to $η_{\mathrm{re}}(ω)$ for a wide class of holographic models. This allows us to determine $η_{\mathrm{re}}(ω)$ of a strongly coupled field theory by the black hole metric and the graviton mass. The latter serves as the bulk dual to the translation symmetry breaking on the boundary. We convert the flow equation to a Neural Ordinary Differential Equation (Neural ODE), which is a neural network with continuous depth and produces output through a black-box ODE solver. Testing the Neural ODE on three well-known holographic models without translation symmetry, we demonstrate its ability to accurately learn either the metric or mass when given the other. Additionally, we illustrate that the learned metric can be used to predict the derivative of entanglement entropy $S$ with respect to the size of entangling region $l$.

hep-th↗

arXiv2023

Reconstructing black hole exteriors and interiors using entanglement and complexity

Based on the AdS/CFT correspondence, we study how to reconstruct bulk spacetime metrics by various quantum information measures on the boundary field theories, which include entanglement entropy, mutual information, entanglement of purification, and computational complexity according to the proposals of complexity=volume 2.0 and complexity=generalized volume. We present several reconstruction methods, all of which are free of UV divergence and most of which are driven by the derivatives of the measures with respect to the boundary scales. We illustrate that the exterior and interior of a black hole can be reconstructed using the measures of spatial entanglement and time-evolved complexity, respectively. We find that these measures always probe the spacetime in a local way: reconstructing the bulk metric in different radial positions requires the information at different boundary scales. We also show that the reconstruction method using complexity=volume 2.0 is the simplest and has a certain strong locality.

hep-th↗

arXiv2022

Holographic renormalization by Hamilton-Jacobi formulation with generated ansatz

In AdS/CFT corresponding, the UV divergence of generating functional on the field theory can be removed as the IR divergence in the gravity. This geometric process is well known as holographic renormalization. The standard method of holographic renormalization is based on the Fefferman-Graham expansion, which is strict and universal but technically cumbersome. To improve the technique, different methods have been proposed. Here we develop an alternative approach to holographic renormalization based on the Hamilton-Jacobi formulation of gravity. Compared to previous approaches, its distinguishing feature is the generation of exact ansatz of counterterms. We apply this approach to several typical holographic models, which consistently performs well.

hep-th↗

arXiv2020

Deep learning black hole metrics from shear viscosity

Based on AdS/CFT correspondence, we build a deep neural network to learn black hole metrics from the complex frequency-dependent shear viscosity. The network architecture provides a discretized representation of the holographic renormalization group flow of the shear viscosity and can be applied to a large class of strongly coupled field theories. Given the existence of the horizon and guided by the smoothness of spacetime, we show that Schwarzschild and Reissner-Nordström metrics can be learned accurately. Moreover, we illustrate that the generalization ability of the deep neural network can be excellent, which indicates that by using the black hole spacetime as a hidden data structure, a wide spectrum of the shear viscosity can be generated from a narrow frequency range. These results are further generalized to an Einstein-Maxwell-dilaton black hole. Our work might not only suggest a data-driven way to study holographic transports but also shed some light on holographic duality and deep learning.

hep-th↗

arXiv2019

Hamilton-Jacobi Approach to Holographic Renormalization of Massive Gravity

Recently, a practical approach to holographic renormalization has been developed based on the Hamilton-Jacobi formulation. Using a simple Einstein-scalar theory, we clarify that this approach does not conflict with the Hamiltonian constraint as it seems. Then we apply it to the holographic renormalization of massive gravity. We assume that the shift vector is falling off fast enough asymptotically. We derive the counterterms up to the boundary dimension d=4. Interestingly, we find that the conformal anomaly can even occur in odd dimensions, which is different from the Einstein gravity. We check that the counterterms cancel the divergent part of the on-shell action at the background level. At the perturbation level, they are also applicable in several time-dependent cases.

hep-th↗

arXiv2019

Acoustic black holes in curved spacetime and emergence of analogue Minkowski metric

Gravity is not only able to be mimicked in flat spacetimes, but also in curved spacetimes. We study analogue gravity models in curved spacetime by considering the relativistic Gross-Pitaevskii theory and Yang-Mills theory in the fixed background spacetime geometry. The results show that acoustic metrics can be emergent from curved spacetimes yielding a Hadamard product of a real metric-tensor and an analogue metric-tensor. Taking \emph{quantum vortices} as \emph{test particles}, we evaluate their released energy ratio during the "gravitational binding". The $2+1$-dimensional flat Minkowski metric is derived from the $3+1$-dimensional Anti-de Sitter space by considering perturbations of the Yang-Mills field, which implies that Minkowski spacetime can be also simulated and the derivations presented here have some deep connections with the holographic principle.

hep-th↗

arXiv2018

Holographic complexity of the disk subregion in (2+1)-dimensional gapped systems

Using the volume of the space enclosed by the Ryu-Takayanagi (RT) surface, we study the complexity of the disk-shape subregion (with radius R) in various (2+1)-dimensional gapped systems with gravity dual. These systems include a class of toy models with singular IR and the bottom-up models for quantum chromodynamics and fractional quantum Hall effects. Two main results are: i) in the large-R expansion of the complexity, the R-linear term is always absent, similar to the absence of topological entanglement entropy; ii) when the entanglement entropy exhibits the classic `swallowtail' phase transition, the complexity is sensitive but reacts differently.

hep-th↗

arXiv2018

Collective diffusion and quantum chaos in holography

We define a particular combination of charge and heat currents that is decoupled with the heat current. This `heat-decoupled' (HD) current can be transported by diffusion at long distances, when some thermo-electric conductivities and susceptibilities satisfy a simple condition. Using the diffusion condition together with the Kelvin formula, we show that the HD diffusivity can be same as the charge diffusivity and also the heat diffusivity. We illustrate that such mechanism is implemented in a strongly coupled field theory, which is dual to a Lifshitz gravity with the dynamical critical index z=2. In particular, it is exhibited that both charge and heat diffusivities build the relationship to the quantum chaos. Moreover, we study the HD diffusivity without imposing the diffusion condition. In some homogeneous holographic lattices, it is found that the diffusivity/chaos relation holds independently of any parameters, including the strength of momentum relaxation, chemical potential, or temperature. We also show a counter example of the relation and discuss its limited universality.

hep-th↗

arXiv2018

Holographic RG flow of thermo-electric transports with momentum dissipation

We construct the holographic renormalization group (RG) flow of thermo-electric conductivities when the translational symmetry is broken. The RG flow is probed by the intrinsic observers hovering on the sliding radial membranes. We obtain the RG flow by solving a matrix-form Riccati equation. The RG flow provides a high-efficient numerical method to calculate the thermo-electric conductivities of strongly coupled systems with momentum dissipation. As an illustration, we recover the AC thermo-electric conductivities in the Einstein-Maxwell-axion model. Moreover, in several homogeneous and isotropic holographic models which dissipate the momentum and have the finite density, it is found that the RG flow of a particular combination of DC thermo-electric conductivities does not run. As a result, the DC thermal conductivity on the boundary field theory can be derived analytically, without using the conserved thermal current.

hep-th↗

arXiv2017

Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation

We show that there exists a class of charged BTZ-like black hole solutions in Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ is characterized by a charge-dependent logarithmic term in the metric function. As concrete examples, we give five such charged BTZ-like black hole solutions and the standard charged BTZ metric can be regarded as a special instance of them. In order to check the recent proposed universal relations between diffusivity and the butterfly velocity, we first compute the diffusion constants of the standard charged BTZ black holes and then extend our calculation to arbitrary dimension $d$, exponents $z$ and $θ$. Remarkably, the case $d=θ$ and $z=2$ is a very special in that the charge diffusion $D_c$ is a constant and the energy diffusion $D_e$ might be ill-defined, but $v^2_Bτ$ diverges. We also compute the diffusion constants for the case that the DC conductivity is finite but in the absence of momentum relaxation.

hep-th↗

arXiv2017

Hyperscaling violating black hole solutions and Magneto-thermoelectric DC conductivities in holography

We derive new black hole solutions in Einstein-Maxwell-Axion-Dilaton theory with a hyperscaling violation exponent. We then examine the corresponding anomalous transport exhibited by cuprate strange metals in the normal phase of high-temperature superconductors via gauge/gravity duality. Linear temperature dependence resistivity and quadratic temperature dependence inverse Hall angle can be achieved. In the high temperature regime, the heat conductivity and Hall Lorenz ratio are proportional to the temperature. The Nernst signal first increases as temperature goes up but it then decreases with increasing temperature in the high temperature regime.

hep-th↗

arXiv2017

Wilsonian RG-flow approach to holographic transport with momentum dissipation

We systematically present a new approach for studying the coupled linear transport of holographic systems. In this approach, the set of equations for the linear perturbations can be reduced to a first-order nonlinear ordinary differential equation expressed as the radial (renormalization group) flow equation of the transport matrices. As an important application, we use this approach to compute the DC and AC conductivities of a holographic model with momentum dissipation, which can be easily read off from the nonlinear flow equations. This method also works for transport in the presence of an external magnetic field.

hep-th↗