A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We simplify and extend a 6D conformal gravity theory to 8D, linking it to Q-curvature.
We use conformal, but ghostful, Weyl gravity to study its ghost-free, second derivative, partially massless (PM) spin 2 component in presence of Einstein gravity with positive cosmological constant. Specifically, we consider both gravitational- and self- interactions of PM via the fully non-linear factorization of conf…
HR in 8D encodes unique conformal gravity with negative curvature.
We propose further conformal parametrizations for initial data in some modified Einstein gravity theories. Some of them give rise to conformally covariant systems.
The configuration space of the reduced Hamiltonian formulation of quantum gravity has been shown, for non-Ricci flat metrics, to be a higher-dimensional analogue of the Teichmüller space of conformal structures on a Riemann surface. In this article we show that the configuration space of conformal connection-dynamics i…
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 …
Length metrics can be closely approximated by conformally flat metrics.
Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].
It is shown that 3D part of a spherically symmetric solution in conformal Weyl gravity interacting with Maxwell electrodynamics is a Yamabe flow as well. The Yamabe flow describes the transition from a horn of an initial wormhole to a 3D Euclidean space both filled with a radial electric field. It is supposed that such…
We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when w…
Twistor space constructions and actions are given for full Yang-Mills and conformal gravity using almost complex structures that are not, in general, integrable. These are used as the basis of a derivation of the twistor-string generating functionals for tree level perturbative scattering amplitudes of Yang-Mills and c…
We propose a model of quantum gravity in arbitrary dimensions defined in terms of the BV quantization of a supersymmetric, infinite dimensional matrix model. This gives an (AKSZ-type) Chern-Simons theory with gauge algebra the space of observables of a quantum mechanical Hilbert space H. The model is motivated by previ…
Proposes a new variational principle for Einstein gravity.
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum grav…
New conformally Einstein metrics on Heisenberg group found.
Fefferman and Graham showed some time ago that four dimensional conformal geometries could be analyzed in terms of six dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit…
The paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.
Physical reasons suggested in \cite{Ha-Ha} for the \emph{Quantum Gravity Problem} lead us to study \emph{type-changing metrics} on a manifold. The most interesting cases are \emph{Transverse Riemann-Lorentz Manifolds}. Here we study the conformal geometry of such manifolds.
New formula connects holographic entanglement entropy to Willmore energy in 5D.
An introduction into the theory of locally anisotropic spaces (modelled as vector bundles provided with compatible nonlinear and distinguished linear connections and metric structures and containing as particular cases different types of Kaluza--Klein and/or extensions of Lagrange and Finsler spaces) is presented. The …
We generalize Penrose's notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Li…
This paper is devoted to the study of the constraint equations of the Lovelock gravity theories. In the case of an empty, compact, conformally flat, time-symmetric, and space-like manifold, we show that the Hamiltonian constraint equation becomes a generalisation of the -Yamabe problem. That is to say, the prescri…
In this article we propose a new geometrization of the radiative phase space of asymptotically flat space-times: we show that the geometry induced on null-infinity by the presence of gravitational waves can be understood to be a generalisation of the tractor calculus of conformal manifolds adapted to the case of degene…
Proves a higher-order positive energy theorem for stationary solutions in fourth-order gravity.
The Willmore energy, alias bending energy or rigid string action, and its variation-the Willmore invariant-are important surface conformal invariants with applications ranging from cell membranes to the entanglement entropy in quantum gravity. In work of Andersson, Chrusciel, and Friedrich, the same invariant arises as…
The paper studies geometric structures in perfect fluid spacetimes with specific metrics.
Characterizes pseudo B-symmetric spacetimes and their implications in f(R) gravity.
We formulate and solve the analog of the universal Conformal Ward Identity for the stress-energy tensor on a compact Riemann surface of genus , and present a rigorous invariant formulation of the chiral sector in the induced two-dimensional gravity on higher genus Riemann surfaces. Our construction of the action f…
We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed s…
The moduli space of isometry classes of Riemannian structures on a smooth manifold was emphasized by J.A.Wheeler in his superspace formalism of quantum gravity. A natural question concerning it is: What is a natural topology on such moduli space that reflects best quantum fluctuations of the geometries within the Planc…
We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. …
Motivated by considerations of euclidean quantum gravity, we investigate a central question of spectral geometry, namely the question of reconstructability of compact Riemannian manifolds from the spectra of their Laplace operators. To this end, we study analytic paths of metrics that induce isospectral Laplace-Beltram…
We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We explicitly work out the ca…
We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure…
We find necessary and sufficient conditions for a Riemannian four-dimensional manifold with anti-self-dual Weyl tensor to be locally conformal to a Ricci--flat manifold. These conditions are expressed as the vanishing of scalar and tensor conformal invariants. The invariants obstruct the existence of parallel …
A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in $\bbR^n$, or $\bbS^n$, $n\in \bbN$, which are distributed according to the configurational microcanonical measure , or rather some regularization thereof, where H is the configu…
In this paper we deal with quadratic metric-affine gravity, which we briefly introduce, explain and give historical and physical reasons for using this particular theory of gravity. Further, we introduce a generalisation of well known spacetimes, namely pp-waves. A classical pp-wave is a 4-dimensional Lorentzian spacet…
"Ends of hyperbolic 3-manifolds should support canonical Wick Rotations, so they realize effective interactions of their ending globally hyperbolic spacetimes of constant curvature." We develop a consistent sector of WR-rescaling theory in 3D gravity, that, in particular, concretizes the above guess for many geometrica…
Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work by Polyakov. In this paper, we investigate the case of simply connected domains…
Introduces a new relation between BF theory and gravity.
We formulate the theory of nearly autoparallel maps (generalizing conformal transforms) of locally anisotropic spaces and define the nearly autoparallel integration as the inverse operation to both covariant derivation and deformation of connections by nearly autoparallel maps. By using this geometric formalism we cons…
PhD dissertation on Finsler geometry and gravity, focusing on Berwald spaces and exact solutions.
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off…
Manifolds endowed with torsion and nonmetricity are interesting both from the physical and the mathematical points of view. In this paper, we generalize some results presented in the literature. We study Einstein manifolds (i.e., manifolds whose symmetrized Ricci tensor is proportional to the metric) in d dimensions wi…
A relation between gravity on Poisson manifolds proposed in arXiv:1508.05706 and Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein-Hilbert-type …
Study boundary structure of gauge fields on AdS spaces.
A differential calculus, differential geometry and the E-R Gravity theory are studied on noncommutative spaces. Noncommutativity is formulated in the star product formalism. The basis for the gravity theory is the infinitesimal algebra of diffeomorphisms. Considering the corresponding Hopf algebra we find that the defo…
We introduce the concept of a base conformal warped product of two pseudo-Riemannian manifolds. We also define a subclass of this structure called as a special base conformal warped product. After, we explicitly mention many of the relevant fields where metrics of these forms and also considerations about their curvatu…