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.
Solves Einstein vacuum equations with specific boundary conditions.
We consider four-dimensional vacuum spacetimes which admit a nonvanishing spacelike Killing field. The quotient with respect to the Killing action is a three-dimensional quotient spacetime . We establish several results regarding maximal hypersurfaces (spacelike hypersurfaces of zero mean curvature) in such quot…
Solves initial boundary value problem for vacuum Einstein equations and proves geometric uniqueness.
Gauging procedure constructs lagrangians for carrollian gravity.
We show that the ``classical'' Harder-Narasimhan filtration associated to a non semistable vector bundle can be viewed as a limit object for the action of the gauge group in the direction of an optimal destabilizing vector. This vector appears as an extremal value of the so called "maximal weight function". We give…
Recent developments in the understanding of supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining four-manifold invariants by counting instantons, one can define equivalent four-manifold invariants by counting solution…
Establishes existence of maximal globally hyperbolic development for Einstein equations.
We develop a systematic approach to G_2 holonomy manifolds with an SU(2)xSU(2) isometry using maximal eight-dimensional gauged supergravity to describe D6-branes wrapped on deformed three-spheres. A quite general metric ansatz that generalizes the celebrated Bryant-Salamon metric involves nine functions. We show that o…
In the double field theory, gauge symmetries are realized as generalized diffeomorphisms in the doubled spacetime. By consistency of the theory, dependence of tensor fields on the doubled coordinates is strongly constrained. This causes finite transformation law highly complicated, both technically and conceptually. In…
Unified view of spectral networks linking geometry and gauge theory.
Narasimhan and Ramadas showed that the Gribov ambiguity was maximal for the product SU(2) bundle over S^3. Specifically they showed that the holonomy group of the Coulomb connection is dense in the connected component of the identity of the gauge group. Instead of base manifold S^3, we consider here a base manifold wit…
We reformulate the compatibility condition between a generalized metric and a small (non-maximal rank) Dirac structure in an exact Courant algebroid found in the context of the gauging of strings and formulated by means of two connections in purely Dirac-geometric terms. The resulting notion, a transverse generalized m…
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…
Develops a new theory for neural systems stability and width effects.
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…
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.
Extends gauge conditions for superparticle to conic neighbourhood.
Lecture notes on gauge theory for manifold invariants.
The basic financial purpose of an enterprise is maximization of its value. Trade credit management should also contribute to realization of this fundamental aim. Many of the current asset management models that are found in financial management literature assume book profit maximization as the basic financial purpose. …
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…
In this article, we introduce a new method (based on Perelman's lambda-functional) to study the stability of compact Ricci-flat metrics. Under the assumption that all infinitesimal Ricci-flat deformations are integrable we prove: (A) a Ricci-flat metric is a local maximizer of lambda in a C^2,alpha-sense iff its Lichne…
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.
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.
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…