Related papers: Space-time symmetries and the Yang-Mills gradient …

We study the Yang-Mills gradient flow using numerical stochastic perturbation theory. As an application of the method we consider the recently proposed gradient flow coupling in the Schr\"odinger functional for the pure SU(3) gauge theory.

Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We…

Lie symmetry group method is applied to study Newtonian incompressible fluid's equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are…

Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations both…

Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with…

Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…

We show that an infinitesimal step of gradient flow can be used for defining a novel approach for computing gradients of physical observables with respect to action parameters. Compared to the commonly used perturbative expansion, this…

Local products of fields deformed by the so-called Yang--Mills gradient flow become renormalized composite operators. This fact has been utilized to construct a correctly normalized conserved energy--momentum tensor in the lattice…

In K.~Hieda, A.~Kasai, H.~Makino, and H.~Suzuki, Prog.\ Theor.\ Exp.\ Phys.\ \textbf{2017}, 063B03 (2017), a properly normalized supercurrent in the four-dimensional (4D) $\mathcal{N}=1$ super Yang--Mills theory (SYM) that works within…

We formulate and explore the physical implications of a new translation gauge theory of gravity in flat space-time with a new Yang-Mills action, which involves quadratic gauge curvature and fermions. The theory shows that the presence of an…

The introduction of a space-time lattice as a regulator of field theories breaks symmetries associated with continuous space-time, i.e.\ Poincar{\'e} invariance and supersymmetry. A non-zero gluino mass in the supersymmetric Yang-Mills…

We study the gradient flow of the potential energy on the infinite-dimensional Riemannian manifold of spatial curves parametrized by the arc length, which models overdamped motion of a falling inextensible string. We prove existence of…

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these…

Ward-Takahashi identities are nonperturbative relations between correlation functions and arising from symmetries in quantum and statistical fields theories, as Noether currents conservation for classical theories. Since their historical…

Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the nonlinear regime. Whether it be huge formulae, or mountains of numerical data, standard methods of presentation make…

We consider applications of the theory of balanced weight filtrations and iterated logarithms, initiated in arXiv:1706.01073, to PDEs. The main result is a complete description of the asymptotics of the Yang--Mills flow on the space of…

We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $\langle E(t)\rangle$ is used to define a running coupling at a scale given by the linear size of the…

The Yang-Mills gradient flow and the observable E(t), defined by the square of the field strength tensor at t>0, are calculated at finite lattice spacing and tree-level in the gauge coupling. Improvement of the flow, the gauge action and…

We consider general infinite-dimensional dynamical systems with the Galilean and spatiotemporal scaling symmetry groups. Introducing the equivalence relation with respect to temporal scalings and Galilean transformations, we define a…

This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072,…