Future stability of a specific type of Kaluza-Klein spacetime is proven.
problem Stability of a particular class of Kaluza-Klein vacua.
method Einstein flow on a product manifold, Kaluza-Klein reduction, wave map type and Maxwell type equations, slice-adapted gauge.
result Future stability of the Milne universe within the class of spacetimes.
Identifies half-space neighborhoods of pleating rays in the Riley slice of Schottky groups.
problem Determining points in the Riley slice of Schottky groups.
method Adapting ideas from L. Keen and C. Series, identifying half-space neighborhoods of pleating rays.
result Provides a provable method to determine if a point is in the Riley slice.
We find canonical gauges for higher gauge theories in 2- and 3-gauge theories.
problem Finding good gauges for connections in higher gauge theories.
method Defined Coulomb gauges for 2- and 3-connections in strict 2- and 3-gauge theories.
result Coulomb gauges are essentially unique and linear in critical dimensions.
Paper introduces Tensor Gauge Flow Models for better data encoding.
problem Lack of expressive flow dynamics in existing Generative Flow Models.
method Incorporates higher-order Tensor Gauge Fields into the Flow Equation.
result Tensor Gauge Flow Models achieve improved generative performance.
L-CNNs preserve gauge symmetry in lattice simulations.
problem Breaking gauge symmetry in neural network models.
method Lattice gauge equivariant convolutional neural networks (L-CNNs).
result L-CNNs represent gauge invariant functions on the lattice.
Develops a new approach to describe gauge theories with background fields using presymplectic structures.
problem Describing gauge theories with background fields using presymplectic structures.
method Extension of the presymplectic BV-AKSZ approach to include background fields.
result Gauge theories with background fields correspond to presymplectic gauge PDEs over gauge PDEs describing background fields.
L-CNNs learn gauge invariant quantities on lattices.
problem Learning gauge invariant quantities on lattices.
method Novel convolutional layer preserving gauge equivariance and forming Wilson loops.
result L-CNNs can approximate any gauge covariant function on the lattice.
L-CNNs preserve gauge symmetry in neural networks.
problem Applying machine learning to lattice gauge theory while preserving gauge symmetry.
method L-CNNs use gauge equivariance to construct a gauge equivariant convolutional layer and bilinear layer.
result L-CNNs achieve higher accuracy in non-linear regression tasks compared to non-equivariant CNNs.
New discretization method for gauge theories preserves gauge invariance rigorously.
problem Discretization of continuum gauge theories with polynomial curvature.
method Holonomy-based discretization preserving gauge invariance.
result Gauge-fixing is fully rigorous for discretized Yang-Mills theories.
When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equat…
Defines gauge transformations for Jacobi structures and their effects on contact groupoids.
problem Understanding transformations of Jacobi structures and their implications.
method Definition and discussion of gauge transformations for Jacobi structures and their impact on contact groupoids.
result Gauge transformations affect the contact structure of contact groupoids.
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∞-structures we show that, under certain technical conditions, algebraic gauge theories can be transferred along chain contractions. Sp…
We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver bundles, and show that the reduced quiver gauge theories are all generically buil…
We consider gauged twistor spinors which are supersymmetry generators of supersymmetric and superconformal field theories in curved backgrounds. We show that the spinor bilinears of gauged twistor spinors satify the gauged conformal Killing-Yano equation. We prove that the symmetry operators of the gauged twistor spino…
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
problem Applying convolutional neural networks to non-Abelian lattice gauge theories while preserving gauge symmetry.
method Developed a geometric formulation of L-CNNs that are equivariant under global symmetries and gauge transformations.
result Convolutional operations in L-CNNs are a specific case of gauge-equivariant neural networks on SU(N) principal bundles. Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.
problem Improving generative model performance.
method Integrates a learnable Gauge Field into Flow ODEs.
result Gauge Flow Models outperform traditional Flow Models in Flow Matching experiments.
Extends gauge conditions for superparticle to conic neighbourhood.
problem Applying gauge conditions to superparticle in momentum space.
method Patching gauge conditions over different parts of field space.
result Extension of light-cone gauge to conic neighbourhood.
Lecture notes on gauge theory for manifold invariants.
problem Constructing invariants of manifolds using gauge theory.
method Gauge-theoretic approach to manifold invariants.
result Introduction to Seiberg-Witten gauge theory.
The Kuperberg invariant is shown to be gauge invariant for certain framed 3-manifolds.
problem Exploring gauge invariance of the Kuperberg invariant for specific 3-manifolds.
method Using hyperbolic 3-manifolds and finite-dimensional Hopf algebras.
result First examples of gauge invariants of general finite-dimensional Hopf algebras via topological methods.
Study gauge groups over high-dimensional manifolds, showing homotopy decompositions.
problem Classifying gauge groups over high-dimensional manifolds.
method Combination of manifold topology and homotopy theory techniques.
result Various homotopy decompositions of gauge groups are shown.
The paper gauges non-linear sigma models using Lie algebroid actions.
problem Gauging non-linear sigma models with Lie algebroid actions.
method Proposes gauging non-linear sigma models with Lie algebroid actions and discusses conditions for gauging.
result It is possible to find a set of vector fields which will (locally) admit a Lie algebroid gauging.
We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent in…
We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such as gauge theory, lattice gauge fields, equivariant bundles, etc. In the course o…
Develops a new sampling method for gauge theories.
problem Sampling from SU(N) gauge theories. method Gauge-equivariant flows for SU(N) variables. result Constructs a class of flows respecting matrix conjugation symmetry.
Gauge theory for families helps compare 4-manifold groups.
problem Comparing diffeomorphism and homeomorphism groups of 4-manifolds.
method Gauge theory applied to families of 4-manifolds.
result Improved understanding of group comparisons in 4-manifolds.
New proof of Schwarzschild stability using geometric gauge.
problem Linear stability of Schwarzschild spacetime under gravitational perturbations.
method Employing a new geometric gauge and exploiting the structure of transport equations.
result Established both orbital and asymptotic stability for linearised quantities.
In the first part of this paper, we work out a perturbative Lagrangian formulation of semistrict higher gauge theory, that avoids the subtleties of the relationship between Lie 2-groups and algebras by relying exclusively on the structure semistrict Lie 2-algebra v and its automorphism 2-group Aut(v). Gauge transformat…
A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented. Emphasis is made on the analysis of the perturbative study of the theory and its connection to the theory of Vassiliev invariants. It is described how the study of t…
It is argued that the enlargement of the gauge group found in non-commutative gauge theory is more fundamentally thought of as a consequence of the non-locality of the construction and that it was already encountered in an earlier discussion of a non-local gauge theory.
The paper extends curve curvature types from normed to gauge planes.
problem Extending curve curvature classification to gauge planes.
method Using gauge analogue of Birkhoff orthogonality and differential geometry.
result Four curvature types (Minkowski, normal, circular, arc-length) are identified.
Researchers prove CWY angular momentum is supertranslation invariant in double null gauge.
problem Supertranslation invariance of CWY angular momentum in double null gauge.
method Identified and proved supertranslation ambiguity; showed CWY angular momentum is free of this ambiguity.
result CWY angular momentum is supertranslation invariant in double null gauge.
Survey of gauge theory for families of 4-manifolds.
problem Understanding gauge theory for families of 4-manifolds.
method Developed gauge theory for diffeomorphism groups of 4-manifolds.
result New applications of gauge theory to diffeomorphism groups.
We study the relation between the space of representation classes of the fundamental group of a Riemann surface and gauge theory on trivalent graphs. We construct a partial gauge fixing in the latter gauge theory. As an application we get a proof of a conjecture of Florentino.
Higher Gauge Flow Models integrate higher geometry and symmetries into Generative Flow Models.
problem Improving generative models' performance.
method Integrates L∞-algebra into Generative Flow Models, leveraging higher geometry and symmetries. result Substantial performance improvements on Gaussian Mixture Model datasets.
Survey on advanced gauge theory concepts.
problem Understanding higher gauge theory structures.
method Introduction to higher structures and connections on higher principal bundles.
result Summarized applications and principles of higher gauge theories.
Researchers solved Einstein-Yang-Mills equations for arbitrary gauge groups.
problem Analyzing spacetime metrics and gauge fields with specific symmetries.
method Analytically integrated Einstein-Yang-Mills equations for a general gauge group.
result Solved Einstein-Yang-Mills equations for arbitrary gauge groups.
We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds introducing thus the concept of equivariant Q-cohomology. Using this concept we desc…
The Bogomol'nyi-Prasad-Sommerfield (BPS) multi-wall solutions are constructed in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Exact solutions are obtained with full generic moduli for infinite gauge coupling and with partial moduli for finite …
Unified approach to data processing using gauge theory.
problem Data representation and analysis with consistent symmetry.
method Geometric gauge theory for discrete vector bundles.
result Unified understanding of heat kernel properties and data transformation.
Symmetry operators of twistor spinors and harmonic spinors can be constructed from conformal Killing-Yano forms. Transformation operators relating twistors to harmonic spinors are found in terms of potential forms. These constructions are generalized to gauged twistor spinors and gauged harmonic spinors. The operators …
Gauge symmetries explain the emergence of Merton-Garman equation from Black-Scholes in finance.
problem Understanding the emergence of Merton-Garman equation from Black-Scholes in financial markets.
method Using Hamiltonian formulation and gauge symmetry to derive the Merton-Garman equation from Black-Scholes, analyzing the role of stochastic volatility.
result Gauge symmetry explains the appearance of stochastic volatility and its massivation via the Higgs mechanism.
The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac sigma models can be obtained from a gauging procedure adapted to Lie algebroids in …
Extends Coulomb gauge existence to non-associative gauge theory.
problem Existence of configurations with divergence-free torsion in non-associative gauge theory.
method Analyzes non-associative gauge theory based on smooth loops and their tangent algebras, proving existence of configurations with divergence-free torsion.
result Proves existence of configurations with divergence-free torsion given a sufficiently small torsion in a Sobolev norm.
Study gauge theory of real and quaternionic parabolic bundles over real curves.
problem Examining gauge theoretic aspects of real and quaternionic parabolic bundles over real curves.
method Investigate orbits of connections under gauge groups for fixed real or quaternionic structures.
result Gauge-theoretic quotients of real or quaternionic connections are inside the real points of moduli of holomorphic bundles.
Transforms classical connections using pushforwards and gauge transformations.
problem Transforming classical connections in categorical settings.
method Constructing pushforwards and applying gauge transformations to decorated path spaces.
result Combines traditional gauge transformation with affine translation.
Paper untwists gauge fields, linking two bundles.
problem Dealing with two symmetry groups in gauge theories.
method Isomorphism between twisted and standard gauge fields on different bundles.
result Local twisted fields can be used in standard gauge theories.
Complete set of local gauge invariants for Kerr spacetime identified.
problem Identifying all local gauge invariant quantities for linearized gravity on Kerr spacetime.
method Constructing a complete compatibility complex for the Killing operator and demonstrating equivalence with first compatibility operator.
result Any gauge invariant quantity for linearized gravity on Kerr can be expressed in terms of identified gauge invariants and their derivatives.
In this note, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk-Mrcun and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely res…