Extends decay estimates for Yang-Mills-Higgs fields on Minkowski and de Sitter spacetimes.
problem Decay rates of Yang-Mills-Higgs fields on Minkowski and de Sitter spacetimes.
method First worked on Minkowski space, localized estimates, then used conformal transformations to extend to Einstein cylinder and de Sitter space.
result Extended exponential decay rates for Yang-Mills-Higgs fields on de Sitter space and inverse polynomial decay rates on Minkowski space.
Sharp decay estimate for Yang-Mills-Higgs fields near singular points.
problem Non-removable singularities in Yang-Mills-Higgs fields.
method Sharp asymptotic decay estimate near singular points.
result Decay rate determined by limit holonomy.
The paper studies decay near singularities of 3d Yang-Mills-Higgs fields.
problem Understanding isolated singularities of 3d Yang-Mills-Higgs fields.
method Derives decay estimates and applies removable singularity theorems.
result Generalizes removable singularity theorems for 3d Yang-Mills-Higgs fields.
Removes singularities for Yang-Mills-Higgs fields in higher dimensions.
problem Yang-Mills-Higgs fields with isolated singularities.
method Establishes decay estimates and conformally invariant energy bounds.
result Removable singularity theorem for Yang-Mills-Higgs fields.
Study shows rapid decay of Hitchin metric from semi-flat metric on Higgs bundles.
problem Analyzing the asymptotic behavior of the Hitchin metric on moduli spaces of Higgs bundles.
method Examined the decay rate of the difference between Hitchin and semi-flat metrics on smooth spectral curves.
result Exponential decay of the difference between Hitchin and semi-flat metrics as t approaches infinity.
Study on finite energy SU(2) monopoles on AC 3-manifolds, proving integrality of charge and curvature decay.
problem Understanding the asymptotic behavior of finite energy SU(2) monopoles on AC 3-manifolds.
method Analysis of critical points of the SU(2) Yang--Mills--Higgs energy on asymptotically conical 3-manifolds.
result Proves integrality of the monopole number and quadratic decay of curvature, among other findings.
Study improves the exponential rate of metric difference in Higgs bundles.
problem Improving the exponential rate of metric difference in Higgs bundles.
method Analyzes the Hitchin metric and semi-flat metric in rank two Higgs bundles.
result Exponential rate of metric difference is improved.
Study describes metrics on moduli space of Higgs bundles, proving exponential decay rate.
problem Analyzing the geometry of moduli space of Higgs bundles.
method Perturbing from approximate solutions to describe metrics, comparing to semi-flat metrics.
result Proves exponential decay rate of gL2−gsf=O(e−γt). Machine learning identifies jet substructure from boosted Higgs decays.
problem Distinguishing jets from boosted heavy particles from QCD jets.
method Spectral analysis using neural networks on angular scale.
result ANN of angular spectrum input performs similarly to existing taggers.
Improved ANN-based Monte Carlo simulation for Higgs decay events.
problem Accurate simulation of Higgs boson decay events.
method Monte Carlo simulation using an Artificial Neural Network (ANN) with improved training algorithm.
result The ANN simulation of Higgs decay is within 0.7% of the true value and achieves 26% unweighting efficiency.
This paper tackles class imbalance in high energy physics experiments.
problem Extracting a signal from a large background in high energy physics experiments.
method Overview of class imbalance techniques and case studies.
result Demonstrates the effectiveness of class imbalance techniques in high energy physics experiments.
Paper shows existence of vortex solutions with specific decay properties.
problem Existence of solutions to Seiberg-Witten equations with specific decay properties.
method Dimensional reduction of Seiberg-Witten equations on the plane.
result Contains both exponentially decayed and polynomial growth solutions.
The paper proves unique blow-down for critical points of a Yang-Mills-Higgs functional.
problem Proving uniqueness of blow-down for critical points of a Yang-Mills-Higgs functional.
method Using an Allard-type improvement of flatness to establish co-dimension-two analogue of Savin's theorem.
result Entire critical points have unique blow-down, two-dimensional in ambient dimensions 2-4 or any dimension assuming local minimizer.
Study quadratic one-forms on logarithmic Higgs bundles on pointed curves.
problem Quadratic one-forms on logarithmic Higgs bundles on pointed curves.
method Use elementary pole cancellation for invariant polynomials.
result Found a logarithmic quadratic one-form.
We give conditions on a general stress-energy tensor T_{αβ} in a spherically symmetric black hole spacetime which are sufficient to guarantee that the black hole will contain a (spherically symmetric) marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Price law decay p…
Novel framework speeds up physics simulations for beyond-standard-model research.
problem Efficiently infer complex physics models from large-scale simulations.
method Probabilistic programming framework that couples to simulators, using neural network for inference compilation.
result Achieved inference efficiency at a fraction of Markov chain Monte Carlo cost.
Growth of spinors in 4D and 3D generalized Seiberg-Witten equations.
problem Proving growth of spinors in GSW equations on R4 and R3. method Unified framework of GSW equations, averaged L2-norm, curvature decay assumption, Yang-Mills-Higgs energy. result Growth of spinors in GSW equations on R4 and R3 faster than a power of the radius under suitable curvature decay. Iterative subtraction method outperforms other feature ranking techniques in high-energy physics.
problem Determining the most important features for classification in high-energy physics experiments.
method Comparison of feature ranking methods including Iterative Addition, Iterative Removal, and BDT Selection Frequency.
result Iterative Removal method is the most efficient for feature ranking in classification tasks.
Artificial neural networks typically have a fixed, non-linear activation function at each neuron. We have designed a novel form of piecewise linear activation function that is learned independently for each neuron using gradient descent. With this adaptive activation function, we are able to improve upon deep neural ne…
Boosted decision trees improved for particle identification in high-energy physics.
problem Overfitting in boosted decision trees hampers their performance in particle identification.
method Meta-learning techniques of boosting and bagging to mitigate overfitting.
result The proposed algorithm achieves performance close to that of deep neural networks on a benchmark data set.
We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initi…
Paper studies convergence of Yang-Mills-Higgs flow on Kähler manifolds.
problem Analyzing convergence of Yang-Mills-Higgs flow for twisted Higgs pairs.
method Proves convergence to a reflexive twisted Higgs sheaf outside a closed subset.
result Limiting twisted Higgs sheaf is isomorphic to the double dual of graded twisted Higgs sheaves.
Classifies Higgs and co-Higgs bundles on symmetric spaces.
problem Classifying Higgs and co-Higgs bundles over Hermitian symmetric spaces.
method Defined homogeneous principal Higgs and co-Higgs bundles, provided a classification up to isomorphism.
result Defined and classified moduli spaces for each type of bundle.
In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional for Higgs pairs on a Hermitian vector bundle (E,H0) over a compact Kähler manifold (M,ω). We study the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity, and show that the limiting Higgs sheaf is isomorph…
We study the basic properties of Higgs sheaves over compact Kähler manifolds and we establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is semistable. Then, we use the flattening theorem to construct a regularization of a…
In this paper, we introduce some notions on the pair consisting of a Chern connection and a Higgs field closely related to the first and second variation of Yang-Mills- Higgs functional, such as strong Yang-Mills-Higgs pair, degenerate Yang-Mills-Higgs pair, stable Yang-Mills-Higgs pair. We investigate some properties …
The paper studies the moduli space of Higgs pairs and their geometric properties.
problem The moduli space of Higgs pairs and its geometric properties.
method Introduced τ-stability of Higgs pairs and established the Kobayashi-Hitchin correspondence. result Proved that the moduli space is a non-singular complex manifold for a suitable choice of τ. Study on deforming complex manifolds and Higgs bundles.
problem Deforming holomorphic-Higgs pairs on complex manifolds.
method Introduced a DGLA and derived the Maurer-Cartan equation to govern the deformation.
result Proved the local completeness of the Kuranishi family of the deformed holomorphic-Higgs pair.
Higgs bundles used in new applications.
problem None explicitly stated in the abstract.
method Overview of recent applications.
result Applications of Higgs bundles.
Improved sensitivity to Higgs potential through neural simulation-based inference for di-Higgs events.
problem Improving sensitivity to physics beyond the Standard Model through di-Higgs events.
method Simulation-based inference using neural networks to estimate per-event likelihood ratios.
result Adding kinematic observables improves experimental sensitivity to Higgs self-coupling.
The paper examines critical points in Higgs bundle moduli spaces.
problem Understanding critical points in Higgs bundle moduli spaces.
method Analyzes the Higgs field vanishing on divisors and related integrable systems.
result Topological and differential-geometric properties of critical loci are addressed.
Researchers extend Higgs bundle theory to parabolic bundles, counting components.
problem Counting components in moduli spaces of Higgs bundles with parabolic structures.
method Generalized Beauville-Narasimhan-Ramanan correspondence, Bott-Morse theory.
result Exact component count for maximal parabolic Sp(2n,ℝ)-Higgs bundles.
Study finds conditions for minimum of Donaldson's functional on Higgs bundles with non-holomorphic Higgs fields.
problem Finding conditions for minimum of Donaldson's functional on Higgs bundles with non-holomorphic Higgs fields.
method Restriction of Donaldson's functional to diagonal metrics on Higgs bundles with non-holomorphic Higgs fields.
result Provides necessary and sufficient conditions for the functional to attain a minimum.
We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle (E,H0) over a Riemann surface X. It is already known the gradient flow with initial data (A0,φ0) converges to a critical point (A∞,φ∞) of this functional. Using a modified Chern-Wei…
The paper solves equations for Higgs bundles on non-Kähler manifolds.
problem Analytically stable Higgs bundles on non-Kähler manifolds.
method Solving the Hermitian-Einstein equation on analytically stable Higgs bundles under specific conditions.
result Solutions to the Hermitian-Einstein equation for analytically stable Higgs bundles on non-Kähler manifolds.
On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized geometry coincides with that of co-Higgs bundle when the generalized complex manifold is ordinary complex. Schwarzenberger's r…
NSBI approach detects Higgs trilinear coupling with high luminosity upgrade constraints.
problem Determining the Higgs trilinear self-coupling via off-shell Higgs production.
method Hybrid neural simulation-based inference (NSBI) incorporating SMEFT and quantum interference effects.
result NSBI achieves sensitivity close to theoretical optimum for Higgs trilinear self-coupling.
In this article, we study the Higgs vector bundles (E,θ) over a compact Calabi-Yau manifolds X. We use Yang-Mills-Higgs flow to prove that if a semistable Higgs bundle with vanishing Chern classes over a compact connected Calabi-Yau manifold, then the Higgs field θ is trivial. In particular, the vector bundle E…
Researchers can retrieve Yang-Mills-Higgs fields from Minkowski space measurements.
problem Retrieving Yang-Mills-Higgs fields from active local measurements in Minkowski space.
method Exploiting non-linear wave interactions and Lie algebra structure.
result Yang-Mills-Higgs fields can be retrieved from source-to-solution data.
Classifies very stable Higgs bundles for complex groups.
problem Classifying Higgs bundles for arbitrary complex groups.
method Classification based on stability and Higgs field properties.
result Extends previous classification for GLn to arbitrary groups.
Study co-Higgs sheaves on toric varieties, finding explicit examples.
problem Characterizing and understanding co-Higgs sheaves on toric varieties.
method Characterization and explicit computation of examples.
result Explicit examples of co-Higgs sheaves on toric varieties computed.
The paper examines Yang-Mills-Higgs pairs on vector bundles and proves stability and energy identity.
problem Stability and energy identity of Yang-Mills-Higgs pairs on vector bundles.
method Bubble-neck decomposition and analysis of weakly stable pairs.
result A sequence of Yang-Mills-Higgs pairs converges to a Yang-Mills-Higgs pair with uniformly bounded energy.
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line C, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to TxP1.…
Study on harmonic metrics for rank 3 Higgs bundles in Hitchin section.
problem Finding compatible harmonic metrics for rank 3 Higgs bundles in the Hitchin section.
method Defined a symmetric pairing and studied spectral curves as 2-sheeted branched coverings.
result Gave a condition for Higgs bundles on C or C∗ to have compatible harmonic metrics. We review the notion of Gieseker stability for torsion-free Higgs sheaves. This notion is a natural generalization of the classical notion of Gieseker stability for torsion-free coherent sheaves. We prove some basic properties that are similar to the classical ones for torsion-free coherent sheaves over projective alge…
The paper defines and analyzes higher-order Yang-Mills-Higgs functionals and their gradient flows.
problem Analyzing the behavior of higher-order Yang-Mills-Higgs functionals and their gradient flows.
method Gauge fixing technique, L2-bound of the Higgs field, local L2-derivative estimates, energy estimates, blow-up analysis. result Solutions to the gradient flow do not hit finite time singularities under certain conditions.
Study uses Vinberg pairs for Higgs bundles, revealing their role.
problem Understanding the role of Vinberg pairs in Higgs bundle theory.
method Exploring Vinberg pairs defined by cyclic gradings of a Lie algebra in Higgs bundle theory.
result Vinberg pairs play a significant role in Higgs bundle theory.
Study finds obstacles to solutions for specific equations on compact surfaces.
problem Existence of solutions to self-dual equations on compact surfaces.
method Depends on Higgs field zeroes and vortex number.
result Infinitely many Higgs fields for which solutions cannot exist.