We discuss from a geometric point of view the connection between the renormalization group flow for non--linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field theories. In particular we argue that the structure of Ricci flow singularities suggests…
On-device research index
arXiv research
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.
169,181 papers · 148 categories
Trend · papers per month
48 results for “renormalized connections”
We compute renormalized curvature integrals on Poincaré-Einstein manifolds.
problem Computing renormalized curvature integrals on Poincaré-Einstein manifolds.
method General procedure that connects Gauss-Bonnet-type formulas and identifies scalar conformal invariants.
result Explicit conformally invariant Gauss--Bonnet-type formulas for compact Einstein manifolds.
Study saddle connections on hyperelliptic surfaces, finding growth rates.
problem Count saddle connections on hyperelliptic surfaces without interior intersections.
method Used horocycle renormalization to prove lower bound growth rate.
result Found saddle connections satisfy growth rate.
A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a metric structure, when gravitational models with infinite many couplings reduce…
The paper introduces new CR invariants for pseudo-Einstein manifolds.
problem Constructing CR invariants for pseudo-Einstein manifolds.
method Applying Cheeger-Simons differential characters to a modified normal tractor connection.
result Identifies differential characters with renormalized connections and derives formulas for characteristic numbers.
We calculate the asymptotic behavior of hyperbolic volume and Chern-Simons invariant.
problem Calculating the asymptotic behavior of hyperbolic volume and Chern-Simons invariant.
method Renormalization of the Chern-Simons invariant using asymptotics along an equidistance foliation.
result The leading coefficient introduces a complex-valued quantity consisting of mean curvature and torsion 2-form.
Study examines the geometry of a group of Fourier-integral operators related to Diff(S^1).
problem Investigating the geometry of a specific group of Fourier-integral operators.
method Defined a right-invariant pseudo-Riemannian metric on the group using renormalized traces of pseudo-differential operators.
result Extended the Hilbert-Schmidt Riemannian metric to the group.
Defines a new geometric quantity for hyperbolic manifolds, showing it's well-defined and invariant.
problem Defining a mass for asymptotically hyperbolic manifolds under weaker conditions.
method Volume-renormalized mass defined as a linear combination of ADM mass and renormalized volume.
result Volume-renormalized mass is well-defined and diffeomorphism invariant under weaker conditions.
New method renormalizes neural network Gaussian processes to identify learnable vs. unlearnable modes.
problem Separating learnable from unlearnable information in neural networks.
method Wilsonian renormalization applied to Gaussian Process Regression.
result Obtains a universal flow of the ridge parameter that becomes input-dependent.
Neural Network Renormalization Groupcond-mat.stat-mech
A neural network RG approach for efficient collective variable identification.
problem Identifying mutually independent collective variables in complex systems.
method A variational RG approach using normalizing flows and neural nets to map physical configurations to latent variables with reduced mutual information.
result Direct access to the renormalized energy function of latent variables for unbiased training and efficient sampling.
A new RG approach connects discrete and continuous time descriptions of Gaussian processes.
problem Discretization of continuous stochastic processes for accurate simulation or model inference.
method Renormalization Group (RG) approach for Gaussian time series generated by auto-regressive models.
result RG fixed points correspond to discretizations of linear SDEs, providing insights into process accuracy.
After analyzing renormalization schemes on a Poincaré-Einstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is well-known, and we show any scalar Riemannian invariant renormalizes similarly. We consider characteristic forms and their behavior und…
Minimal surfaces in hyperbolic space have a renormalized area criterion.
problem Minimal surfaces in hyperbolic space
method Renormalized area criterion
result Y must be a totally geodesic disk
Study shows continuity of renormalized volume in geometric limits.
problem Continuity of renormalized volume in geometric limits of hyperbolic manifolds.
method Analyzing sequences of convex-cocompact hyperbolic manifolds and their renormalized volumes.
result Renormalized volume is continuous under geometric limits.
Study uses renormalized area to determine metric expansion from minimal surfaces.
problem Recovering the expansion of asymptotically hyperbolic metrics from minimal surfaces.
method Uses renormalized area functional on minimal submanifolds to recover metric expansion.
result Proves rigidity for log-analytic metrics and determines obstruction tensor.
Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spacesmath.DG
Defines renormalized volume for bounded regions in asymptotically hyperbolic Einstein spaces.
problem Calculating the volume of bounded regions in complex geometries.
method Defines renormalized volume, proves Gauss-Bonnet theorem, computes derivative under variations.
result Derives a Gauss-Bonnet theorem for the renormalized volume.
Study calculates the renormalized area of catenoids in hyperbolic spaces.
problem Calculating the renormalized area of catenoids in hyperbolic spaces.
method Variational characterization and Chern--Gauss--Bonnet formulas for locally conformally flat manifolds.
result Renormalized area of catenoids varies continuously from negative infinity to twice the area of totally geodesic hypersurfaces.
We discuss in rather general terms quantum field theories dealing with spaces of maps between Riemannian manifolds. In particular we explore the well--known connection between the renormalization group flow for non--linear sigma models and the Ricci flow.
New Bayesian method uses momentum-space renormalization for image modeling.
problem Bayesian image modeling challenges in Gaussian graphical models.
method Combines marginal likelihood maximization with momentum-space renormalization.
result Scheme for computing hyperparameters and mean square errors.
Defines and proves properties of weighted renormalized volume coefficients.
problem None explicitly stated; focuses on mathematical definitions and proofs.
method Defines weighted renormalized volume coefficients and proves their variational nature and polynomial representation.
result Weighted renormalized volume coefficients are variational and can be expressed as polynomials of specific tensors.
We study the critical points of the renormalized volume for acylindrical geometrically finite hyperbolic 3-manifolds that include rank-1 cusps, and show that the renormalized volume is locally convex around these critical points. We give a modified definition of the renormalized volume that is additive under gluing, an…
For a strictly pseudoconvex domain in a complex manifold we define a renormalized volume with respect to the approximately Einstein complete Kähler metric of Fefferman. We compute the conformal anomaly in complex dimension two and apply the result to derive a renormalized Chern--Gauss--Bonnet formula. Relations between…
We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the -curvature. We show how all t…
Researchers define and analyze the renormalized volume of 4D Ricci-flat ALE spaces.
problem Understanding the properties of 4D Ricci-flat ALE spaces.
method Introducing a new definition of renormalized volume and proving its properties.
result The renormalized volume is always less than or equal to zero, with equality for specific spaces.
We define and study the renormalized volume for geometrically finite hyperbolic -manifolds, including with rank- cusps. We prove a variation formula, and show that for certain families of convex co-compact hyperbolic metrics $g_\eps$ degenerating to a geometrically finite hyperbolic metric with rank- cus…
We interpret the physical -field renormalization group flow in the language of Courant algebroids, clarifying the sense in which this flow is the natural "Ricci flow" for generalized geometry. Next we show that the -field renormalization group flow preserves T-duality in a natural sense. As corollaries we obtain …
New adapted renormalized volume for hyperbolic 3-manifolds with compressible boundary.
problem Analyzing convex co-compact hyperbolic 3-manifolds with compressible boundaries.
method Defining and analyzing a new version of the renormalized volume.
result The adapted renormalized volume is bounded and has properties analogous to the classical renormalized volume.
Paper derives a formula for renormalized area of minimal hypersurfaces in 5D Poincaré-Einstein spaces.
problem Calculating the renormalized area of minimal hypersurfaces in 5D Poincaré-Einstein spaces.
method Derives a Gauss-Bonnet formula for renormalized area in terms of scalar invariants and characterizes minimal hypersurfaces in terms of conformal geometry.
result Derives a formula expressing renormalized area in terms of integrals of scalar Riemannian invariants.
Proves energy expression on Poincaré-Einstein spaces.
problem Computing renormalized Yang-Mills energy on Poincaré-Einstein manifolds.
method Generalizes Chang-Qing-Yang method for renormalized volumes and uses scattering theory for Schrödinger operators.
result Agrees with anomaly boundary integrand in seven dimensions.
New equations for rigid body motion on infinite-dimensional spaces of operators.
problem Integrating rigid body dynamics on infinite-dimensional spaces of operators.
method Introducing pseudo-Riemannian metrics and adapting classical integrability theory.
result Existence of geodesics and integrals of motion for the rigid body equations.
Upper bounds on renormalized volume for Schottky groups derived from extremal lengths.
problem Comparing renormalized volumes of Schottky and Fuchsian manifolds with the same boundary.
method Bounding renormalized volume in terms of genus and extremal lengths of curves on the boundary Riemann surface.
result Upper bounds on renormalized volume for Schottky groups established.
New properties are derived of renormalized volume functionals, which arise as coefficients in the asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) manifold. A formula is given for the renormalized volume of an even-dimensional AHE manifold in terms of an arbitrary totally geodesic compa…
Renormalization in neural networks linked to quantum field theory.
problem Implementing renormalization in neural networks.
method Mapping neural networks to quantum field theory, applying renormalization techniques.
result Changing weight standard deviation corresponds to a renormalization flow.
Formula derived for 4D manifolds with boundary involving renormalized volume and boundary integral.
problem Calculating the Euler characteristic of 4D manifolds with boundary.
method Derives a Chern-Gauss-Bonnet formula for a specific type of metric.
result Sum of renormalized volume and boundary integral is a conformal invariant when boundary is umbilic.
We study the evolution of the renormalized volume functional for asymptotically Poincare-Einstein metrics (M,g) which are evolving by normalized Ricci flow. In particular, we prove that the time derivative of the renormalized volume along the flow is the negative integral of scal(g(t)) + n(n-1) over the manifold. This …
New compactification of Teichmüller space via renormalized volume.
problem Compactify Teichmüller space with new distance.
method Horocompactification with renormalized volume.
result Translation length of pseudo-Anosov mapping classes equals hyperbolic volume of mapping tori.
Formula for tube volume on special geometric manifolds.
problem Calculating volumes of geometric structures.
method Using Einstein constant and polarization volume.
result Formula for renormalized tube volume.
Renormalized pruning improves neural network accuracy.
problem Over-parameterized neural networks waste many parameters.
method Propose renormalizing sparse neural networks.
result Renormalized pruning converges to zero error.
Formula for renormalized area of hypersurfaces in hyperbolic spaces.
problem Calculating the renormalized area of asymptotically minimal hypersurfaces in hyperbolic spaces.
method Combining Chen's conformal invariant quantity and Chern-Gauss-Bonnet formulas.
result Extension of renormalized area formulas to higher dimensions and non-minimal cases.
New method calculates volume-renormalized mass from Hamiltonian perspective.
problem Calculating volume-renormalized mass for asymptotically hyperbolic manifolds.
method Using Michel's mass invariants and a reduced Hamiltonian perspective, the volume-renormalized mass is deduced.
result The reduced Hamiltonian recovers the volume-renormalized mass and its variations.
The paper studies circle packings using renormalization and subdivision rules.
problem Characterizing and proving properties of circle packings with specific subdivision rules.
method Iterations of skinning maps on Teichmüller spaces, renormalization theory, subdivision rules.
result Uniformly contracting renormalization operator and geometric inflexibility of circle packings.
A Sharp Isoperimetric Property of the Renormalized Area of a Minimal Surface in Hyperbolic Spacemath.DG
Minimal surfaces in hyperbolic space have a sharp area bound.
problem Bounding the renormalized area of minimal surfaces.
method Proving an inequality using conformal length of ideal boundary.
result Sharp isoperimetric property of renormalized area.
Volume renormalization for conformally compact asymptotically hyperbolic manifolds in dimension fourmath.DG
We derive a new renormalized volume formula for conformally compact asymptotically hyperbolic manifolds in dimension four. The formula generalizes the ones given by Anderson, Albin, and Chang-Qing-Yang for the case of Poincare-Einstein manifolds. We also derive variational formulas for the renormalized seen as a functi…
Isoperimetric interpretation for the renormalized volume of convex co-compact hyperbolic 3-manifoldsmath.DG
The renormalized volume is reinterpreted using isoperimetric profiles.
problem Understanding the renormalized volume of convex co-compact hyperbolic 3-manifolds.
method Using isoperimetric profiles and Minkowski inequalities.
result A sharp Minkowski inequality for horospherically convex sets in .
The paper generalizes CR invariants using renormalized characteristic forms.
problem Defining new CR invariants via renormalized characteristic forms.
method Introducing new curvatures for each renormalized characteristic form.
result The new curvatures' integrals match CR invariants constructed by Marugame.
Ricci flow emerges from renormalizing nonlinear Sigma models.
problem Understanding the renormalization group flow in nonlinear Sigma models.
method Using Euclidean algebraic quantum field theory and Wick ordering.
result The first-order renormalization group flow of nonlinear Sigma models equals the Ricci flow.
The Gauss-Bonnet Theorem is studied for edge metrics as a renormalized index theorem. These metrics include the Poincaré-Einstein metrics of the AdS/CFT correspondence. Renormalization is used to make sense of the curvature integral and the dimensions of the -cohomology spaces as well as to carry out the heat equa…
Study compares deep learning and RG flow using Ising model.
problem Theoretical explanation of deep learning.
method Statistical mechanics model of Ising model, RBM training, RG treatment.
result Correlation functions show RG-like patterns in deep learning.