Develops a Kaluza-Klein theory in affine spaces without metric.
problem Formalizes a geometric theory of electromagnetic fields in affine spaces.
method Formulates dimensional reduction using principal fiber bundles and Ehresmann connections.
result Shows that non-integrability of horizontal distribution implies nontrivial electromagnetic fields.
Study on curvature properties of exotic 7-sphere using quaternionic geometry.
problem Examining curvature of an exotic 7-sphere.
method Using Kaluza-Klein Ansatz with quaternionic language, focusing on moduli spaces of instantons and metrics.
result Identified a center in the moduli space of k=2 instantons and computed the Ricci tensor for a metric of maximal isometry. We investigate the Kaluza-Klein reductions to ten dimensions of the purely gravitational half-BPS M-theory backgrounds: the M-wave and the Kaluza-Klein monopole. We determine the moduli space of smooth (supersymmetric) Kaluza-Klein reductions by classifying the freely-acting spacelike Killing vectors which preserve som…
We investigate Kaluza-Klein metrics with a recurrent light-like vector field over a pseudo-Riemannian manifold.
Study classifies metrics on anti-de Sitter spacetime with specific symmetries.
problem Classifying metrics with specific symmetries on anti-de Sitter spacetime.
method Used classification techniques for pseudo-Riemannian and almost contact metric structures.
result Obtained classifications of homogeneous structures on anti-de Sitter spacetime.
Global Double Field Theory is a higher-dimensional generalization of Kaluza-Klein theory.
problem Formulating a global theory for higher-dimensional gauge fields.
method Generalizing Kaluza-Klein theory to higher principal bundles and higher gauge fields.
result Higher Kaluza-Klein geometry provides a global formulation for Double Field Theory.
This study explores Kaluza-Klein reductions of new maximally supersymmetric backgrounds.
problem Exploring new maximally supersymmetric backgrounds in five dimensions.
method Classifying Kaluza-Klein reductions to four dimensions and determining preserved supersymmetry.
result Discovery of novel non-homogeneous four-dimensional Lorentzian spacetimes with N=1 supersymmetry. New black hole solutions with lens space horizons in 5D Kaluza-Klein theory.
problem Finding black hole solutions with specific horizon topologies.
method Formally asymptotically flat black hole solutions constructed through Kaluza-Klein reduction.
result Explicit construction of regular black hole solutions with L(p,q) horizons. Equations of motion of low-energy string effective actions can be conveniently described in terms of generalized geometry and Levi-Civita connections on Courant algebroids. This approach is used to propose and prove a suitable version of the Kaluza-Klein-like reduction. Necessary geometrical tools are recalled.
The paper explores Kaluza-Klein theories without assuming a fibration structure.
problem Exploring Kaluza-Klein theories without assuming a fibration structure.
method Variational formulations of gauge theories and Einstein--Yang-Mills equations.
result Classical solutions allow the construction of a manifold X of dimension 4 as physical space-time, leading to solutions of the Einstein--Yang-Mills systems. The paper studies how test particles' mass and charge vary in Kaluza-Klein models.
problem Understanding how test particles' mass and charge change in Kaluza-Klein models.
method Analyzes geodesic motion in a 5D Kaluza-Klein spacetime with background metrics encoding 4D gauge fields and Higgs-like scalars.
result The mass and charge of test particles become variable when traversing regions with massive gauge fields or non-constant Higgs scalars.
We study topological T-duality for spaces with a semi-free S1−action with isolated fixed points. Physically, these correspond to spacetimes containing Kaluza-Klein monopoles. We demonstrate that the physical dyonic coordinate of such spaces has an analogue in our formalism. By analogy with the Dirac monopole, we stu…
New ansatz for generalized Kähler surfaces derived from hyperKähler ansatz.
problem Deriving a new ansatz for generalized Kähler surfaces.
method Generalized Gibbons-Hawking ansatz for nondegenerate Poisson structure with biholomorphic S1 action. result Classification of all complete solutions with smallest symmetry group.
This thesis proposes a global geometric formulation of Extended Field Theories.
problem Global understanding of Extended Field Theories remains an open problem.
method Introducing an atlas for the principal infinity-bundle, unifying metric and higher gauge field.
result Global abelian T-duality and Poisson-Lie T-duality are automatically recovered.
We consider the Einstein flow on a product manifold with one factor being a compact quotient of 3-dimensional hyperbolic space without boundary and the other factor being a flat torus of fixed arbitrary dimension. We consider initial data symmetric with respect to the toroidal directions. We obtain effective Einsteinia…
Expressive quantum circuits are harder to train due to flatter cost landscapes.
problem Designing quantum circuits that are both expressive and trainable.
method Deriving a relationship between expressibility and gradient magnitude, extending barren plateau phenomenon.
result Highly expressive ansätze exhibit flatter cost landscapes, making them harder to train.
We consider Riemannian 4-manifolds (X,gX) with a Spin^c-structure and a suitable circle bundle Y over X such that the Spin^c-structure on X lifts to a spin structure on Y. With respect to these structures a spinor φ on X lifts to an untwisted spinor ψ on Y and a U(1)-gauge field A for the Spin^c-st…
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors --generalizing to one side Kaluza-Klein gauge fields and…
The paper explores how non-Killing fields on internal spaces can produce massive gauge fields with chiral interactions.
problem Traditional Kaluza-Klein models limit gauge fields to Killing vector fields, ignoring chiral interactions.
method Investigates properties of 4D gauge fields linked to non-Killing fields on internal spaces using spin geometry and Riemannian submersions.
result Massive gauge fields linked to non-Killing fields can mix fermions with different masses and have asymmetric couplings to left- and right-handed fermions.
We describe a quaternionic-based Ansatz generalizing the Gibbons-Hawking Ansatz to a class of hyperkähler metrics with hidden symmetries. We then apply it to obtain explicit expressions for gravitational instanton metrics of type Dk.
A new approach to quantum machine learning circuits reduces training difficulties.
problem Challenges in training deep quantum circuits due to flat training landscapes.
method Variable structure approach (VAns) to build ansatzes, applying rules for gate growth and removal.
result VAns successfully mitigates trainability and noise-related issues, improving performance in various applications.
The paper classifies helix curves on a pseudo-Riemannian surface.
problem Classifying helix curves on pseudo-Riemannian surfaces.
method Analyzing geodesic flow vector fields and pseudo-Riemannian metrics.
result All helix curves are circular helixes with constant curvature and torsion.
Study of harmonic maps into principal bundles with applications to magnetic interactions.
problem Understanding harmonic mappings from Riemannian manifolds into principal bundles.
method Characterization and analysis of Kaluza-Klein harmonic maps and generalized magnetic maps.
result Existence and properties of generalized magnetic maps, including non-trivial examples.
Deep QMC ansatzes improve variational QMC accuracy.
problem Improving variational QMC accuracy with neural network ansatzes.
method Analysis of deep neural network ansatzes PauliNet and FermiNet convergence to fixed-node limit.
result Deep QMC ansatzes can reach fixed-node limit with large network sizes.
It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley (BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess solutions whose level surfaces are central quadrics in the space of independent variables (the so-called central quadric ansatz). It was demonstrated that generic solutio…
A homogeneous Gibbons-Hawking ansatz is described, leading to 4-dimensional hyperkahler metrics with homotheties. In combination with Blaschke products on the unit disc in the complex plane, this ansatz allows one to construct infinite-dimensional families of such hyperkahler metrics that are, in a suitable sense, comp…
A 12D spinor encodes fermions in a 4D Kaluza-Klein model.
problem Encoding fermions in a 4D spacetime from a higher-dimensional perspective.
method Using a spacetime P=M4imesK with K=SU(3), encoding fermions in 64 spinor components. result The 64 spinor components couple to Standard Model gauge fields in chiral representations.
MBQC linked to CQCA, yielding efficient Ansätze.
problem Quantum computation efficiency and Ansatz adaptation.
method Relating MBQC to CQCA and constructing Ansätze.
result MBQC Ansätze can lead to different performances on learning tasks.
The harmonic sections of the Kaluza-Klein model can be seen as a variant of harmonic maps with additional gauge symmetry. Geometrically, they are realized as sections of a fiber bundle associated to a principal bundle with a connection. In this paper, we investigate geometric and analytic aspects of a model that combin…
We consider differential operators acting on densities of arbitrary weights on manifold M identifying pencils of such operators with operators on algebra of densities of all weights. This algebra can be identified with the special subalgebra of functions on extended manifold M^. On one hand there is a canonical…
We show that a complete simply-connected hyperkaehler 4-manifold with an isometric triholomorphic circle action is obtained from the Gibbons-Hawking ansatz with some suitable harmonic function.
The paper reviews a correspondence between Double Field Theory and bundle gerbes.
problem Exploring a geometric interpretation of Double Field Theory.
method Interpreting Double Field Theory as a field theory on the total space of bundle gerbes.
result Double Field Theory can be seen as a higher geometric field theory.
Study Ricci flow on CP1-bundles over Kähler-Einstein manifolds.
problem Preserving an initial metric on CP1-bundles.
method Ricci flow on CP1-bundles over a product of Kähler-Einstein manifolds.
result The ansatz is preserved along the Ricci flow.
Barrier methods classify minimal submanifolds in hyperkaehler spaces.
problem Classifying compact minimal submanifolds in hyperkaehler spaces.
method Barrier argument and strong stability condition analysis.
result Results towards a classification of compact minimal submanifolds.
The modified J-flow with Calabi ansatz shows convergence or blow-up behavior based on topological constants.
problem Analyzing the behavior of the modified J-flow with Calabi ansatz.
method Using the Calabi symmetry and studying the singularities of the flow.
result The modified J-flow with Calabi ansatz converges to a solution away from a variety, and blows up along the variety.
Torsions, curvatures, structure equations and Bianchi identities for locally anisotropic superspaces (containing as particular cases different supersymmetric extensions and prolongations of Riemann, Finsler, Lagrange and Kaluza--Klein spaces) are investigated.
Develops methods to solve complex and real Hessian equations.
problem Solving complex and real Hessian equations on various domains.
method Introduces an ansatz to reduce PDEs to systems of ODEs, integrating via abelian integrals.
result Constructs entire solutions of arbitrary subcritical phase for dHYM/LYZ and special Lagrangian equations.
Constructs scalar-flat Kähler metrics with varying conical singularities.
problem Creating scalar-flat Kähler metrics with specific singularities.
method Using LeBrun's ansatz, constructs metrics with varying conical singularities.
result Constructs complete scalar-flat Kähler metrics with prescribed conical singularities.
We discuss the Ricci-flat `model metrics' on C2 with cone singularities along the conic {zw=1} constructed by Donaldson using the Gibbons-Hawking ansatz over wedges in R3. In particular we describe their asymptotic behavior at infinity and compute their energies.
Invariant Kähler metrics on line bundles are derived from the Calabi ansatz.
problem Finding invariant scalar-flat Kähler metrics on line bundles over generalized flag varieties.
method Proved using the Calabi ansatz and uniqueness in each Kähler class.
result Existence of a unique scalar-flat Kähler metric in each Kähler class.
Improved Least-Squares Monte Carlo with finite-difference ansatz.
problem Improving accuracy and stability in option pricing.
method Constructing an ansatz using finite-difference solution for conditional expected continuation payoffs.
result Reduces mean squared error and final pricing error.
The abstract discusses special Lagrangians and their flow, proving conjectures and observing related phenomena.
problem Existence and long-time existence of special Lagrangian representatives and Lagrangian mean curvature flow.
method Gibbons-Hawking ansatz, circle-invariant hyperkaehler 4-manifolds, Calabi-Yau 2-folds, Thomas conjecture, Thomas-Yau conjecture.
result Proves versions of the Thomas conjecture and Thomas-Yau conjecture.
The paper presents new formulations of gauge and gravity theories using dynamical principal bundles.
problem Formulating gauge and gravity theories with a flexible principal bundle structure.
method Original variational formulations of Yang-Mills, Einstein's gravitation, and Kaluza-Klein theories with a dynamical principal bundle.
result The principal bundle structure and connection emerge from the dynamics, leading to solutions of Yang-Mills, Einstein-Cartan, or Yang-Mills-Einstein equations.
In this paper, a complete analysis of symmetries and conservation laws for the charged squashed Kaluza--Klein black hole spacetime in a Riemannian space is discussed. First, a comprehensive group analysis of the underlying space-time metric using Lie point symmetries are presented and then it the n-dimensional optima…
The quadric ansatz solves dKP equations in arbitrary dimensions, leading to Einstein-Weyl structures.
problem Characterizing solutions of the dispersionless KP equation in arbitrary dimensions.
method Quadric ansatz for the dKP equation, constructing Einstein-Weyl spaces.
result Explicit new family of Einstein-Weyl spaces constructed and characterized.
Bootstrap bounds on Einstein manifolds using semidefinite programming.
problem Bounding geometric data of closed Einstein manifolds.
method Semidefinite programming applied to consistency conditions of geometric data.
result Bootstrap bounds translate to constraints on Kaluza-Klein modes.
A general approach to formulation of supergravity in higher order anisotropic superspaces (containing as particular cases different supersymmetric extensions and prolongations of Riemann, Finsler, Lagrange and Kaluza--Klein spaces) is given. We analyze three models of locally anisotropic supergravity.
We give a dynamical description, in terms of a Weil-type zeta function, to the holomorphic torsion with coefficients for certain compact Hermitian locally symmetric manifolds, whose connected group G of isometries of the universal cover has only one conjugacy class of cuspidal maximal parabolic subgroup and satisfies a…