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.
Developed a new symmetric hyperbolic formulation for Einstein-Yang-Mills system.
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…
We review quantum field theory approach to the knot theory. Using holomorphic gauge we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way which can be programmed on a computer. We discuss experimental results and temporal …
A new principle minimizes residual and introduces momentum to improve PDE solution dynamics.
Continuous symmetries and their breaking play a prominent role in contemporary physics. Effective low-energy field theories around symmetry breaking states explain diverse phenomena such as superconductivity, magnetism, and the mass of nucleons. We show that such field theories can also be a useful tool in machine lear…
We prove that refined analytic torsion on a manifold with boundary is an analytic section of the determinant line bundle over the representation variety. As a fundamental application we establish a gluing formula for refined analytic torsion on connected components of the complex representation space which contain a un…
Paper introduces Tensor Gauge Flow Models for better data encoding.
L-CNNs preserve gauge symmetry in lattice simulations.
Develops a new approach to describe gauge theories with background fields using presymplectic structures.
L-CNNs learn gauge invariant quantities on lattices.
L-CNNs preserve gauge symmetry in neural networks.
We study the problem of finding good gauges for connections in higher gauge theories. We find that, for -connections in strict -gauge theory and -connections in -gauge theory, there are local "Coulomb gauges" that are more canonical than in classical gauge theory. In particular, they are essentially unique,…
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…
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 -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.
Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.
The Kuperberg invariant is shown to be gauge invariant for certain framed 3-manifolds.
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…
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…
Develops a new sampling method for gauge theories.
Gauge theory for families helps compare 4-manifold groups.
New proof of Schwarzschild stability using geometric gauge.
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…
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.
Survey of gauge theory for families of 4-manifolds.
We define gauge transformations of Jacobi structures on a manifold. This is related to gauge transformations of Poisson structures via the Poissonization. Finally, we discuss how the contact structure of a contact groupoid is effected by a gauge transformation of the Jacobi structure on its base.
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.
Researchers prove CWY angular momentum is supertranslation invariant in double null gauge.
Higher Gauge Flow Models integrate higher geometry and symmetries into Generative Flow Models.
Machine learning improves sub-hourly precipitation data recovery.
Survey on advanced gauge theory concepts.
This paper examines a proposal for gauging non-linear sigma models with respect to a Lie algebroid action. The general conditions for gauging a non-linear sigma model with a set of involutive vector fields are given. We show that it is always possible to find a set of vector fields which will (locally) admit a Lie alge…
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.
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.
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.
Transforms classical connections using pushforwards and gauge transformations.
Study gauge theory of real and quaternionic parabolic bundles over real curves.
The homotopy theory of gauge groups has received considerable attention in recent decades. In this work, we study the homotopy theory of gauge groups over some high dimensional manifolds. To be more specific, we study gauge groups of bundles over -connected closed -manifolds, the classification of which was …
Paper untwists gauge fields, linking two bundles.
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…
Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent formalism and in local coordinates. These are the gauge fields needed for the con…
Higher gauge theory via differential nonabelian cohomology