arXiv research

Complete set of local gauge invariants for Kerr spacetime identified.

Proves stability of Schwarzschild black holes, showing metric coefficients decay.

L-CNNs learn gauge invariant quantities on lattices.

Proves boundedness and decay for spin 1 Teukolsky equation on Reissner-Nordström spacetime.

The Kuperberg invariant is shown to be gauge invariant for certain framed 3-manifolds.

Study linearized Schwarzschild spacetimes, proving decay of master quantities.

In this paper we argue that when gauge invariance is taken into consideration, there is no consistent geometric framework of Finsler class that can accommodate Randers type spaces. In this context, an alternative non-Finslerian framework for Randers spacetimes compatible with gauge invariance is introduced.

Proves boundedness and decay for spin 2 Teukolsky system on Reissner-Nordström spacetime.

Researchers construct a gauge-invariant energy functional for axially symmetric perturbations around Kerr black holes.

New metrics for surface shapes incorporating curve properties.

New discretization method for gauge theories preserves gauge invariance rigorously.

L-CNNs preserve gauge symmetry in lattice simulations.

New gauge invariants from framed 3-manifolds match Hopf algebra indicators.

A new method recovers latent potentials from graph flows, preserving ordering and stability.

New proof of Schwarzschild stability using geometric gauge.

Derives equations for gravitational and electromagnetic perturbations of Reissner-Nordström spacetime.

Formula calculates volume of CMC surfaces with translational periods, disproving isoperimetric conjecture.

Let $C\to M$ be the bundle of connections of a principal bundle on $M$. The solutions to Hamilton-Cartan equations for a gauge-invariant Lagrangian density $Λ$ on $C$ satisfying a weak condition of regularity, are shown to admit an affine fibre-bundle structure over the set of solutions to Euler-Lagrange equations for …

A gauge-invariant form of the nonlinear Hodge equations is studied.

We introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential $m$-form $Ω_m$ with the coefficients satisfying the Plücker relations, which is gauge-invariantly closed and its gauge-invariant coordinates (ratios of coefficients) are (locally) holomorphic with respect to…

Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describ…

We present a gauge invariant generalization of Maxwell's equations and p-form electromagnetism to Kaehler spacetimes.

A projective geometry is an equivalence class of torsion free connections sharing the same unparametrised geodesics; this is a basic structure for understanding physical systems. Metric projective geometry is concerned with the interaction of projective and pseudo-Riemannian geometry. We show that the BGG machinery of …

We study the boundary conditions in the topologically twisted Chern-Simons matter theories with the Lie 3-algebraic structure. We find that the supersymmetric boundary conditions and the gauge invariant boundary conditions can be unified as the complexified gauge invariant boundary conditions which lead to the supergro…

Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action functional. Coupling to scalar fields requires possibly nonlinear representatio…

Abstract properties of hypersurface data analyzed in spherical symmetry.

Researchers extend knot theory formulas to non-rectangular cases.

Study on instability of extreme Reissner-Nordström spacetime perturbations.

Researchers study spectral asymmetry using pseudodifferential projections on the massless Dirac operator.

Solves Einstein vacuum equations gluing problem for close Minkowski data.

Novel discretization method for Yang-Mills theory on the plane.

New method for directed graphs using learnable spectral positional encodings.

A new method for spectral positional encodings in directed graphs using Hermitian block Krylov subspaces.

A large class of variational equations for geometric objects is studied. The results imply conformal monotonicity and Liouville theorems for steady, polytropic, ideal flow, and the regularity of weak solutions to generalized Yang-Mills and Born-Infeld systems.

We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to our setting, is also proved.

Defines risk-free portfolios and risk-free rate using gauge symmetries.

This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather than inheriting it from pre-shape space, and using it to formulate a path energ…

We prove in this paper the linear stability of the celebrated Schwarzschild family of black holes in general relativity: Solutions to the linearisation of the Einstein vacuum equations around a Schwarzschild metric arising from regular initial data remain globally bounded on the black hole exterior and in fact decay to…

In this paper we establish the equivalence of solutions between Schrödinger map into $\mathbb{S}^2$ or $\mathbb{H}^2$ and their associated gauge invariant Schrödinger equations. We also establish the existence of global weak solutions into $\mathbb{H}^2$ in two space dimensions. We extend these ideas for maps into com…

Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space $H_1$. Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Mar…

Machine learning finds a compact fixed point action for SU(3) gauge theory.

Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms $Ω_{N-1}$ of rank N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these flows, given by the systems of the N-1 quasi-linear differential equations, describe coisotropic deform…

This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey ex…

We study a formulation of the standard Poisson sigma model in which the target space Poisson manifold carries the Hamilton action of some finite dimensional Lie algebra. We show that the structure of the action and the properties of the gauge invariant observables can be understood in terms of the associated target spa…

Investigates geometric aspects of double field theory and its membrane sigma-model formulation.

The boundary-value problem for Laplace-type operators acting on smooth sections of a vector bundle over a compact Riemannian manifold with generalized local boundary conditions including both normal and tangential derivatives is studied. The condition of strong ellipticity of this boundary-value problem is formulated. …

We propose a general notion of algebraic gauge theory obtained via extracting the main properties of classical gauge theory. Building on a recent work on transferring curved $A_{\infty}$-structures we show that, under certain technical conditions, algebraic gauge theories can be transferred along chain contractions. Sp…

Upper bounds for magnetic Laplacian eigenvalues on planar domains.