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.
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
Harmonic gauge simplifies geometric analysis of Riemannian metrics.
New proof of Schwarzschild stability using geometric gauge.
We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the problem of classification of principal fibre bundles, which is important for the …
Geometrically describes pseudo-gauge freedom in relativistic hydrodynamics.
Paper introduces Tensor Gauge Flow Models for better data encoding.
In this article we give the realization of the Klein's Program for geometrical structures (Riemannian spaces and fiber bundles with connection) with arbitrary variable curvature within the framework of infinite deformed groups. These groups generalize gauge groups to the case of nontrivial action on the base space of b…
Unified approach to data processing using gauge theory.
Classifies solutions in multisymplectic field theories using geometric gauge freedom.
In this paper we discuss the mechanism of spontaneous symmetry breaking from the point view of vacuum pairs, considered as ground states of a Yang-Mills-Higgs gauge theory. We treat a vacuum as a section in an appropriate bundle that is naturally associated with a minimum of a (general) Higgs potential. Such a vacuum s…
Study on symmetries of differential equations using gauge transformations and coverings.
We consider the deformation theory of two kinds of geometric objects: foliations on one hand, pre-symplectic forms on the other. For each of them, we prove that the geometric notion of equivalence given by isotopies agrees with the algebraic notion of gauge equivalence obtained from the -algebras governing …
In this paper we argue that when gauge invariance is taken into consideration, there is no consistent geometric framework of Finsler class that can accommodate Randers type spaces. In this context, an alternative non-Finslerian framework for Randers spacetimes compatible with gauge invariance is introduced.
Solves initial boundary value problem for vacuum Einstein equations and proves geometric uniqueness.
Proposes a new CNN for meshes that can handle orientation.
The abstract discusses constructing 3d N=2 gauge theories using surgeries and M5-branes.
Higher gauge theory via differential nonabelian cohomology
Study of symmetries in 2D Yang-Mills theory, including orbifolds and higher forms.
The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.
Review of instantons in noncommutative gauge theories across 4, 6, and 8 dimensions.
A description of how a theory of gravity can be considered as a gauge theory (in the sense of Trautman) of the Poincare' group is given. As a result, it is shown that a gauge theory of this kind is consistent with the Equivalence Principle only if the Lagrangian and the constraints are preserved not only by the gauge t…
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…
A geometric construction for obtaining a prolongation of a connection to a connection of a bundle of connections is presented. This determines a natural extension of the notion of canonical energy-tensor which suits gauge and gravitational fields, and shares the main properties of the energy-tensor of a matter field in…
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…
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…
Research characterizes intersection cohomology groups of gauge theories and cotangent bundles.
Develops a new approach to describe gauge theories with background fields using presymplectic structures.
Investigates connections in Lie group bundles, focusing on geometric reduction.
Compactification of M- / string theory on manifolds with structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a three-manifold of ADE singularities. Generic gauge theory solutions include a non-trivial g…
The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge invariance of the construction, need to satisfy particular compatibility conditions. This paper analyzes these compatibilitie…
This paper is motivated by recent developments of higher gauge theory. Different from its style of using higher category theory, we try to describe the concept of higher parallel transport within setting of classical principal bundle theory. From this perspective, we obtain a global geometric proof on a generalized 3-d…
A new geometric metric identifies true data changes from parametrization artifacts in high-dimensional representations.
The problem of gauging a closed form is considered. When the target manifold is a simple Lie group G, it is seen that there is no obstruction to the gauging of a subgroup H\subset G if we may construct from the form a cocycle for the relative Lie algebra cohomology (or for the equivariant cohomology), and an explicit g…
The Poisson--Weil sigma model, worked out by us recently, stems from gauging a Hamiltonian Lie group symmetry of the target space of the Poisson sigma model. Upon gauge fixing of the BV master action, it yields interesting topological field theories such as the 2--dimensional Donaldson-Witten topological gauge theory a…
We present a clear-cut example of the importance of the functorial approach of gauge-natural bundles and the general theory of Lie derivatives for classical field theory, where the sole correct geometrical formulation of Einstein (-Cartan) gravity coupled with Dirac fields gives rise to an unexpected indeterminacy in t…
New gauge preserves Einstein metrics' interactions, proving rigidity on negatively curved manifolds.
The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories of sheaves on moduli spaces of (flat) bundles on algebraic curves. Three years …
This paper develops a geometric framework for Wilson surfaces in higher gauge theory.
Study connections on Lie and Courant algebroids, defining basic curvature and Atiyah cocycle.
Weyl's 1918 geometry proposal revisited in modern physics.
Measuring supernova neutrinos removes spacetime's conformal freedom.
This article is an expanded version of talks given by the authors in Oberwolfach, Bochum, and at the Fano Conference in Torino. Some new results (e. g. the material concerning flag varieties, Quot spaces over , and the generalized quiver representations) were included. The main goal is the construction of gauge th…
We study the propagation of bosonic strings in singular target space-times. For describing this, we assume this target space to be the quotient of a smooth manifold by a singular foliation on it. Using the technical tool of a gauge theory, we propose a smooth functional for this scenario, such that the p…
We give a brief introduction to the Gauge Theory of Arbitrage. Treating a calculation of Net Present Values (NPV) and currencies exchanges as a parallel transport in some fibre bundle, we give geometrical interpretation of the interest rate, exchange rates and prices of securities as a proper connection components. Thi…
Study quantum aspects of 1-form symmetries using BV-BRST cohomology.
The geometric non-linear Schrodinger equation (GNLS) on the complex Grassmannian manifold M is the Hamiltonian equation for the energy functional on C(R,M) with respect to the symplectic form induced from the Kahler form on M. It has a Lax pair that is gauge equivalent to the Lax pair of the matrix non-linear Schroding…
Study quantum aspects of 1-form symmetries using BV-BRST cohomology and gerbes.
Develops a new geometric formulation for abelian gauge theories.