Related papers: The Yang-Mills gradient flow and renormalization
Recently, the Yang-Mills gradient flow is found to be a useful concept not only in lattice simulations but also in continuous field theories. Since its smearing property is similar to the Wilsoninan "block spin transformation", there might…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
We explicitly construct parameter transformations between gradient flows in metric spaces, called curves of maximal slope, having different exponents when the associated function satisfies a suitable convexity condition. These…
We determine the non-perturbative corrections to the gauge coupling constant and the topological charge in the Yang Mills theory. The method makes no explicit use of instanton calculations but instead relies on boundary properties of the…
We lay the foundations of a Morse homology on the space of connections on a principal $G$-bundle over a compact manifold $Y$, based on a newly defined gauge-invariant functional $\mathcal J$. While the critical points of $\mathcal J$…
The gradient-flow formalism is applied to a non-Abelian gauge theory with scalar and fermionic particles, dubbed "scalar QCD". It is shown that the flowed scalar quark requires a field renormalization, albeit only beyond the one-loop level.…
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…
I discuss various situations in which perturbative expansions are used in Yang-Mills theories with asymptotic freedom and establish the limits of its applicability.
We explore the properties of a recently proposed background independent exact renormalization group approach to gauge theories and gravity. In the process we also develop the machinery needed to study it rigorously. The proposal comes with…
We study the BRST renormalization of an alternative formulation of the Yang-Mills theory, where the matrix-propagator of the gluon and the complementary fields is diagonal. This procedure involves scalings as well as non-linear mixings of…
We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed…
A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in…
We review the application of bosonic string techniques to the calculation of renormalization constants and effective actions in Yang-Mills theory. We display the multiloop string formulas needed to compute Yang-Mills amplitudes, and we…
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…
Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows.…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
The Yang-Mills gradient flow is considered on the four dimensional torus T^4 for SU(N) gauge theory coupled to N_f flavors of massless fermions in arbitrary representations. The small volume dynamics is dominated by the constant gauge…
The well-known phase structure of the two-dimensional sine-Gordon model is reconstructed by means of its renormalization group flow, the study of the sensitivity of the dynamics on microscopic parameters. Such an analysis resolves the…
We study the most general renormalization transformations for the first-order formulation of the Yang-Mills theory. We analyze, in particular, the trivial sector of the BRST cohomology of two possible formulations of the model: the standard…
I review my explanation of the irreversibility of the renormalization-group flow in even dimensions greater than two and address new investigations and tests.