Related papers: The gradient flow running coupling scheme
Using a finite volume Gradient Flow (GF) renormalization scheme with Schr\"odinger Functional (SF) boundary conditions, we compute the non-perturbative running coupling in the range $2.2 \lesssim {\bar g}_\mathrm{GF}^2(L) \lesssim 13$.…
We report on the determination of the gradient flow scales in $N_f=2+1$ QCD using highly improved staggered quark (HISQ) ensembles generated by the HotQCD Collaboration for bare gauge couplings ranging from $\beta = 6.423$ to $8.400$. Using…
The gradient flow equation is derived in four-dimensional N=1 supersymmetric Yang-Mills theory in terms of the component field of the Wess-Zumino gauge. We show that the flow-time derivative and supersymmetry transformation that is naively…
The gradient flow of the Yang-Mills action acts pointwise on closed loops of gauge fields. We construct a topologically nontrivial loop of SU(2) gauge fields on S4 that is locally stable under the flow. The stable loop is written explicitly…
We propose a generalization of the gradient flow equation for quantum field theories with nonlinearly realized symmetry. Applying the equation to $\mathcal{N}=1$ $SU(N)$ super Yang-Mills theory in four dimensions, we construct a…
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…
The gradient flow method is a renormalization scheme in which the gauge field is flowed by the diffusion equation. The gradient flow scheme has benefits that the observables composed of flowed gauge fields do not require further…
A novel method to study the bulk thermodynamics in lattice gauge theory is proposed on the basis of the Yang-Mills gradient flow with a fictitious time t. The energy density (epsilon) and the pressure (P) of SU(3) gauge theory at fixed…
We investigate the renormalization group (RG) flow of SU(3) lattice gauge theory in a two coupling space with couplings $\beta_{11}$ and $\beta_{12}$ corresponding to $1\times 1$ and $1\times 2$ loops respectively. Extensive numerical…
We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that…
The use of the Yang-Mills gradient flow in step-scaling studies of lattice QCD is expected to lead to results of unprecedented precision. Step scaling is usually based on the Schr\"odinger functional, where time ranges over an interval…
We use lattice simulations and the continuous renormalization-group method, based on the gradient flow, to calculate the $\beta$ function and anomalous dimensions of the SU(3) gauge theory with $N_f=10$ flavors of fermions in the…
We study SU(2) gauge theory with two fermion flavors in the adjoint representation. Using a clover improved HEX smeared action and the gradient flow running coupling allows us to simulate with larger lattice size than before. We find an…
We test here our recently introduced new lattice method for the $\beta$-function defined over infinite Euclidean space-time in the continuum from scale changes generated by infinitesimal or finite steps of the renormalized gauge coupling on…
The partition function of four dimensional Euclidean, non-supersymmetric SU(2) Yang--Mills theory is calculated in the perturbative and weak coupling regime i.e. in a small open ball about the flat connection (what we call the vicinity of…
In the last few years, the Yang--Mills gradient flow was shown to be an attractive tool for non-perturbative studies of non-Abelian gauge theories. Here a simple extension of the flow to the quark fields in QCD is considered. As in the case…
We study the topological charge distribution of the SU(3) Yang--Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo…
We develop a methodology based on out-of-equilibrium simulations to mitigate topological freezing when approaching the continuum limit of lattice gauge theories. We reduce the autocorrelation of the topological charge employing open…
A gradient flow equation for $\lambda\phi^{4}$ theory in $D=4$ is formulated. In this scheme the gradient flow equation is written in terms of the renormalized probe variable $\Phi(t,x)$ and renormalized parameters $m^{2}$ and $\lambda$ in…
We study the one-loop renormalisation of 4d SU(N) Yang-Mills theory with $M$ adjoint representation scalar multiplets. We calculate the coupled one-loop renormalization group flows for this theory by developing an algebraic description,…