Space-time symmetries and the Yang-Mills gradient flow

Abstract

The recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In this paper we introduce infinitesimal translations along the gradient flow for gauge theories, and study the corresponding Ward identities. This approach is readily generalized to the case of gauge theories defined on a lattice, where the regulator breaks translation invariance. The Ward identities in this case lead to a nonperturbative renormalization of the energy-momentum tensor. We discuss an application of this method to the study of dilatations and scale invariance on the lattice.

29 pages

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• Studying the gradient flow coupling in the Schrödinger functional
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Cited by in corpus (50)

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• Nonperturbative Regulator for Chiral Gauge Theories?
• The nucleon electric dipole moment with the gradient flow: the $\theta$-term contribution
• Energy-momentum tensor on the lattice: non-perturbative renormalization in Yang--Mills theory
• Thermodynamics in quenched QCD: energy--momentum tensor with two-loop order coefficients in the gradient flow formalism
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• Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model
• Gradient Flow of O(N) nonlinear sigma model at large N
• Short flow-time coefficients of CP-violating operators
• Perturbative renormalization of the electric field correlator
• Proof of the renormalizability of the gradient flow
• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory
• Viscosity of pure-glue QCD from the lattice
• Stochastic quantisation of Yang-Mills-Higgs in 3D
• Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow
• The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box
• Stochastic quantisation of Yang-Mills
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• (2+1)-flavor QCD Thermodynamics from the Gradient Flow
• Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
• The Gradient Flow Coupling in Minimal Walking Technicolor
• Supersymmetric gradient flow in the Wess-Zumino model
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• Flow Equation of N=1 Supersymmetric O(N) Nonlinear Sigma Model in Two Dimensions
• Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang--Mills supercurrent
• The running coupling of 8 flavors and 3 colors
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• Renormalization of the energy-momentum tensor in three-dimensional scalar $SU(N)$ theories using the Wilson flow
• Open-Boundary Conditions in the Deconfined Phase
• Lattice energy-momentum tensor from the Yang-Mills gradient flow -- a simpler prescription
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• On the $a$-theorem in the Conformal Window