Related papers: Yang-Mills Meets Data
Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in…
Yang--Mills theory in four dimensions is studied by using the Coulomb gauge. The Coulomb gauge Hamiltonian involves integration of matrix elements of an operator P built from the Laplacian and from a first-order differential operator. The…
Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such…
In this article we summarize our efforts in simulating Yang-Mills theories coupled to matter fields transforming under the fundamental and adjoint representations of the gauge group. In the context of composite Higgs scenarios, gauge…
We study a model of quantum Yang-Mills theory with a finite number of gauge invariant degrees of freedom. The gauge field has only a finite number of degrees of freedom since we assume that space-time is a two dimensional cylinder. We…
I articulate and discuss a geometrical interpretation of Yang-Mills theory. Analogies and disanalogies between Yang-Mills theory and general relativity are also considered.
What is the structure of general quantum processes on composite systems that respect a global or local symmetry principle? How does the irreversible use of quantum resources behave under such symmetry principles? Here we employ an…
This paper introduces a geometric mechanics framework for constrained systems on principal bundles through \emph{compatible pairs} $(\mathcal{D}, \lambda)$, addressing fundamental challenges in gauge-constrained physical systems. We…
In the context of F-theory, we study the related eight dimensional super-Yang-Mills theory and reveal the underlying supersymmetric quantum mechanics algebra that the fermionic fields localized on the corresponding defect theory are related…
We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from…
A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing…
We consider two simple criteria for when a physical theory should be said to be "generally covariant", and we argue that these criteria are not met by Yang-Mills theory, even on geometric formulations of that theory. The reason, we show, is…
Maximally supersymmetric (p+1)-dimensional Yang-Mills theory at large N and finite temperature, with possibly compact spatial directions, has a rich phase structure. Strongly coupled phases may have holographic descriptions as black branes…
A class of new nonabelian gauge theories for vector fields on three manifolds is presented. The theories describe a generalization of three-dimensional Yang-Mills theory featuring a novel nonlinear gauge symmetry and field equations for…
An explicit model of fiber bundle with local fibers being disinct copies of vector 3-space is introduced. They are endowed with frames which are used as local isotopic ones. The field local of isotopic frames is considered as gauge field…
Using our recently proposed covariant algebraic approach the heat kernel for a Laplace-like differential operator in low-energy approximation is studied. Neglecting all the covariant derivatives of the gauge field strength (Yang-Mills…
Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular,…
We investigate quantization properties of Hermitian metrics on holomorphic vector bundles over homogeneous compact K\"ahler manifolds. This allows us to study operators on Hilbert function spaces using vector bundles in a new way. We show…
Gauge theories of conformal spacetime symmetries are presented which merge features of Yang-Mills theory and general relativity in a new way. The models are local but nonpolynomial in the gauge fields, with a nonpolynomial structure that…
We develop a geometric framework that characterizes the synchronization problem --- the problem of consistently registering or aligning a collection of objects. The theory we formulate characterizes the cohomological nature of…