Causal holography reconstructs manifold properties from scattering data.
problem Reconstructing manifold properties from scattering data.
method Introducing metrics of gradient type and using scattering maps.
result Reconstruction of manifold's homology, Gromov simplicial semi-norm, and fundamental group.
The paper explores holographic structures on exotic spheres and their implications.
problem Understanding holographic structures on exotic spheres.
method Introducing and studying holographic structures on closed manifolds Y. result Generalizing the Holography Theorem to fillable holographic structures on Y. The notion of a causal boundary for a spacetime has been a controversial topic during the last three decades. Moreover, recently the role of the boundary in the AdS/CFT correspondence for plane waves, have stimulated its redefinition with some possible alternatives. Our aim is threefold. First, to review the different …
We study smooth {\sf traversing} vector fields v on compact manifolds X with boundary. A traversing v admits a Lyapunov function f:X→R such that df(v)>0. We show that the trajectory spaces T(v) of {\sf traversally generic} v-flows are {\sf Whitney stratified spaces}, and thus admit tr…
Study Liouville action on quasi-Fuchsian groups, proving formulas and relating to holography.
problem Analyzing Liouville action for quasi-Fuchsian groups with different types of elements.
method Derived formulas for classical Liouville action, proved first and second variations, and established holography principle.
result Established an equality linking Liouville action and renormalized volume for quasi-Fuchsian groups.
New method uses equivariant volume for gravitational extremization in holography.
problem Formulating gravitational extremization problems in holography.
method Equivariant volume of internal geometry or cone over it.
result Validates gravitational block formulas for M5 and D4 branes.
Max flow/min cut theorem extended to currents and topology.
problem Continuous max flow/min cut theorem for complex domains.
method Continuous analogue of max flow/min cut theorem considering topology.
result Continuous max flow/min cut theorem proven for currents and laminations.
Holographic reconstruction over local fields using Radon transform.
problem Holographic reconstruction of quantum fields in anti-de Sitter space over local fields.
method Novel construction of Radon transform and its inverse on anti-de Sitter space over local fields.
result Holographic bulk reconstruction can be formulated as the inverse Radon transform.
Holographic energy equals Hamiltonian energy.
problem Equating holographic and Hamiltonian energies.
method Relative holographic and Hamiltonian energy comparison.
result Holographic energy is identical to Hamiltonian energy.
Study Yang-Mills connections on conformally compact manifolds, proving existence of extensions.
problem Existence of Yang-Mills connections on conformally compact manifolds.
method Proving existence of Yang-Mills connections for small deformations.
result Confirming the existence of Yang-Mills connections in the interior of the manifold.
Paper constructs a complex from flow data, capturing manifold's structure.
problem Understanding flows on manifolds with boundaries.
method Origami map from disk to CW-complex, reconstructing manifold's topology.
result Compact CW-complex homotopy equivalent to manifold X. Generalizes holographic method to higher codimension submanifolds.
problem Extract higher-order local invariants of embeddings.
method Natural generalization of holographic method to higher codimension submanifolds.
result New invariants obstructing the order-by-order construction of unit defining maps.
Study of potential Carroll structures and special Carrollian manifolds for null hypersurfaces.
problem Understanding intrinsic geometry of null hypersurfaces.
method Initiate study of potential Carroll structures and explore their relationship to special Carrollian manifolds.
result Initiate the study of potential Carroll structures and their relationship to special Carrollian manifolds.
Krasnov (arXiv: hep-th/0005106) identified the renormalized volume of a Schottky 3-manifold with the action of the Liouville theory on the conformal infiinity. We try to compute the renormalized volume in terms of more transparent geometric quantities.
Deep learning tackles low-photon nanoscale holographic phase retrieval.
problem Low-photon imaging challenges at nanoscale.
method Dataset-free deep learning framework with physical model integration.
result Significantly improves signal recovery from higher noise levels.
We rigorously define the Liouville action functional for finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that the classical action - the critical point of the Liouville action functional, considered as a funct…
New shift operators in conformal geometry simplify proofs and unify theories.
problem Understanding and proving properties of Q-curvatures in conformal geometry. method Introducing shift operators and their compositions, linking to holography and residue families.
result Alternative descriptions and new proofs of Q-curvatures in even dimensions. Let S be a smooth rational curve on a complex manifold M. It is called ample if its normal bundle is positive. We assume that M is covered by smooth holomorphic deformations of S. The basic example of such a manifold is a twistor space of a hyperkahler or a 4-dimensional anti-selfdual Riemannian manifold X (n…
We show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: The holographic counterterms induced near anisotropic infinity take the form of the action for gravity at a Lifshitz point, with the appropriate …
This thesis explores Weyl geometry and quantum anomalies in holography and gauge theories.
problem Understanding Weyl geometry and quantum anomalies in holographic and gauge theories.
method Generalized Weyl-covariant holography, Lie algebroid encoding of BRST complex, and Lie algebroid cohomology.
result Weyl obstruction tensors are used to compute Weyl anomalies and provide geometric insights into quantum anomalies.
The paper recovers contact forms from boundary data using vector fields and Lyapunov functions.
problem Recovering contact forms from boundary data.
method Using vector fields and Lyapunov functions, the paper describes boundary data and proves reconstruction of (X,β) up to diffeomorphism. result Boundary data allow for the reconstruction of (X,β) up to a diffeomorphism of X. New formalism solves kinematical constraints in curved backgrounds and non-trivial states.
problem Solving kinematical constraints due to Weyl invariance in curved backgrounds and non-trivial states.
method Constructing Weyl covariant geometric objects and identifying them as building blocks of correlation functions.
result Exact agreement with thermal OPEs and holographic computations for thermal 2-point functions.
I'll describe a general geometric setup allowing for a generalization of Rehren duality to asymptotically anti-de Sitter spacetimes whose classical matter distribution is sufficiently well-behaved as to prevent the occurence of singularities in the sense of null geodesic incompleteness. I'll also comment on the issues …
We argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization …
The Schwarzian action is linked to the area of Epstein curves in hyperbolic geometry.
problem Understanding the relationship between the Schwarzian action and geometric properties of curves.
method Applying Epstein's construction to relate the Schwarzian action to the area of Epstein curves in hyperbolic disk.
result The Schwarzian action is equivalent to the logarithm of the bi-local observable in Schwarzian field theory.
New method defines conformal geodesics using surfaces in higher-dimensional manifolds.
problem Defining conformal geodesics in a novel way.
method Using surfaces in higher-dimensional manifolds and tractor calculus.
result Conformal geodesics are critical points of renormalized area in higher-dimensional spaces.
Study geodesic flows, billiards, and metrics on manifolds.
problem Inverse scattering and billiard dynamics on Riemannian manifolds.
method Lyapunov function, harmonizing metrics, isoperimetric inequalities, Santaló-Chernov formulas.
result Holography theorems and formulas for geodesic and billiard dynamics.
Holographic method calculates boundary terms in conformal anomaly.
problem Boundary terms modify conformal anomaly in various dimensions.
method Holographic calculation of boundary terms in two prescriptions.
result Identifies exact structure of boundary terms in d=3 and d=4. We describe the asymptotic behavior of minimal area submanifolds in product spacetimes of an asymptotically hyperbolic space times a compact internal manifold. In particular, we find that unlike the case of a minimal area submanifold just in an asymptotically hyperbolic space, the internal part of the boundary submanif…
The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…
Topological twist of gauge theories mapped to AdS/CFT.
problem Mapping topological gauge theories to holographic duals.
method Asymptotically locally hyperbolic solutions to gauged supergravity.
result Partition function independence under AdS/CFT.
Study uses holography to analyze entanglement entropy in deformed CFTs.
problem Analyzing entanglement entropy in $Tar{T}$-deformed CFTs.
method Holographic methods and direct bulk gravitational action evaluation.
result Agreement with known results for entanglement entropy.
Study reveals how boundary wave operator determines metric properties on anti-de Sitter spacetimes.
problem Determining metric properties on anti-de Sitter spacetimes.
method Analysis of Klein-Gordon equation and Dirichlet-to-Neumann map.
result Determines the Taylor series of the bulk metric at the boundary.
Holographic Neural Architectures learn representations from data.
problem Representation learning in deep learning.
method Holographic Neural Architectures (HNAs) derive Holographic Representations from training data.
result HNAs are effective for generative networks, regression, and noise resistance.
Study gauged supergravity, M5-branes, and class R theories, constraining supergravity coefficients and calculating partition functions.
problem Constraints and calculations in higher-derivative supergravity and related theories.
method Holography, Chern-Simons theory, 3d-3d correspondence, wrapped M5-branes.
result Constrained coefficients in supergravity Lagrangian, calculated partition functions for class R theories.
New framework learns disentangled causal representations from observed labels.
problem Learning meaningful disentangled causal representations from observed data.
method ICM-VAE framework using flow-based diffeomorphic functions and causal disentanglement prior.
result Induces highly disentangled causal factors and improves robustness.
Reinterprets Granger causality with causal Bayesian networks and Reichenbach's principles.
problem Lack of a rigorous causal foundation in Granger causality.
method Reinterpreting Granger causality through Reichenbach's principles and causal Bayesian networks, implementing as c-GC.
result c-GC provides a more principled framework for causal discovery in observational datasets.
New measures for causal entropy and information gain studied.
problem Quantifying causal relationships in machine learning.
method Formal study of causal entropy and information gain.
result Established fundamental properties and relationships.
We quantify causal bias in continuous treatment settings.
problem Identifying and quantifying causal bias in continuous treatment scenarios.
method Developed a novel characterization of causal bias in structural causal models, proving conditions for zero bias and efficient estimation.
result Causal bias can be estimated efficiently under certain structural equation restrictions, allowing for causal regularization of predictive models.
Improved Granger causality method for dynamic time series data.
problem Traditional Granger causality method assumes constant causalities, failing to model dynamic causalities.
method Dynamic window-level Granger causality (DWGC) method with causality indexing.
result Improved DWGC method better detects window-level causalities.
The study examines causal razors and their logical relations, highlighting a dilemma in causal discovery.
problem Selecting a reasonable scoring criterion for causal discovery algorithms.
method Review and logical comparison of numerous causal razors, focusing on parameter minimality in multinomial models.
result Parameter minimality poses a dilemma in selecting a reasonable scoring criterion for causal discovery algorithms.
CIB compresses variables causally, preserving key causal interactions.
problem Constructing causal variable abstractions in complex systems.
method Causal Information Bottleneck (CIB) method, extending IB to include causal structures.
result CIB produces causally interpretable abstractions that accurately capture causal relations.
Study b-6j symbols linking anti-de Sitter tetrahedra to hyperbolic geometry.
problem Analyzing b-6j symbols for quantum invariants. method Examining asymptotics and analytic extensions of 6j-symbols. result Connection between anti-de Sitter tetrahedra and hyperbolic geometry.
Paper characterizes and represents pairwise causal background knowledge for improved causal inference.
problem Improving causal inference by handling pairwise causal constraints.
method Graphical characterization, direct causal clause (DCC), unified representation, MPDAG, polynomial-time algorithms.
result Pairwise causal background knowledge uniquely decomposes into MPDAG and DCCs, improving causal effect identification.
Python toolbox uncovers causal relationships from data.
problem Discovering causal relationships from observational data.
method End-to-end approach using algorithms from 'Bnlearn' and 'Pcalg', including pairwise causal discovery.
result Recovery of direct dependencies and causal relationships.
A new method clusters heterogeneous subgroups for accurate causal learning.
problem Diverse causal relationships across different time spans, regions, or strategies.
method Nonlinear Causal Kernel Clustering
result Reduction in prediction error through enhanced causal learning.
Framework for Granger causality in extreme events.
problem Identifying causal links from extreme events in time series.
method Causal tail coefficient and novel inference method.
result Framework outperforms state-of-the-art methods in detecting Granger causality in extremes.
Proposes DCNAR for dynamic causal inference from neural time series.
problem Uncertainty and evolution of causal structure in real-world domains.
method Two-stage neural causal modeling integrating discovery and inference.
result Dynamic causal inferences are more stable and meaningful than alternatives.