Related papers: The Yang-Mills gradient flow and renormalization
We discuss the algebraic renormalization of the Yang--Mills gauge field theory in the presence of translations. Due to the translations the algebra between Sorella's $\d$--operator, the exterior derivative and the BRST--operator closes.…
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…
In this work, we present a new approach to analyze the gradient flow for a positive semi-definite matrix denoising problem in an extensive-rank and high-dimensional regime. We use recent linear pencil techniques of random matrix theory to…
We study the failure of the smoothness of flow maps for the $(1+3)$ dimensional Yang-Mills system in the Lorenz gauge by Knapp type counterexamples. This shows a gap between the scaling critical regularity exponents and the best attainable…
We systematically analyze the effective action on the moduli space of (2,0) superconformal field theories in six dimensions, as well as their toroidal compactification to maximally supersymmetric Yang-Mills theories in five and four…
A simplified version of Higher Covariant Derivative regularization for Yang-Mills theory is constructed. This may make Higher Covariant Derivative method more attractive for practical calculations.
Using renormalization group methods we calculate the derivative expansion of the effective Lagrangian for a covariantly constant gauge field in curved spacetime. Curvature affects the vacuum, in particular it could induce phase transitions…
We approach the problem of learning continuous normalizing flows from a dual perspective motivated by entropy-regularized optimal transport, in which continuous normalizing flows are cast as gradients of scalar potential functions. This…
The field of artificial neural network (ANN) training has garnered significant attention in recent years, with researchers exploring various mathematical techniques for optimizing the training process. In particular, this paper focuses on…
We study the renormalization group flow of higher derivative gravity, utilizing the functional renormalization group equation for the average action. Employing a recently proposed algorithm, termed the universal renormalization group…
In the paper, within the background field method, the renormalization and the gauge dependence is studied as for an SU(2) Yang-Mills theory with multiplets of spinor and scalar fields. By extending the quantum action of the BV-formalism…
Flows on surfaces are one of the most fundamental and classical objects in dynamical systems, and are studied from various areas (e.g. integrable systems, differential equations, fluid mechanics). Though hyperbolic flows and recurrent flows…
In this work, we analyze the relation between reparametrizations of gradient flow and the induced implicit bias in linear models, which encompass various basic regression tasks. In particular, we aim at understanding the influence of the…
We present a formulation of non-Abelian gauge theories in general axial gauges using a Wilsonian (or 'Exact') Renormalisation Group. No 'spurious' propagator divergencies are encountered in contrast to standard perturbation theory. Modified…
A simplified proof of a theorem by Joglekar and Lee on the renormalization of local gauge invariant operators in Yang-Mills theory is given. It is based on (i) general properties of the antifield-antibracket formalism; and (ii)…
Over the last decade the gradient flow formalism became an important tool for lattice simulations of Quantum Chromodynamics. It offers remarkable renormalization properties which pave the way for cross-fertilization between perturbative and…
A class of continuous renormalization group flows with a dynamical adjustment of the propagator is introduced and studied theoretically for fermionic and bosonic quantum field theories. The adjustment allows to include self--energy effects…
Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and…
Given a renormalizable theory we construct the dilatation operator, in the sense of generator of RG flow of composite operators. The generator is found as a differential operator acting on the space of normal symbols of composite operators…
This is a copy of the 2009 Princeton University thesis which examined various aspects of gauge/gravity duality, including renormalization group flows, phase transitions of the holographic entanglement entropy, and instabilities associated…