Continuous renormalization group $\beta$ function from lattice simulations

Abstract

We present a real-space renormalization group transformation with continuous scale change to calculate the continuous renormalization group $\beta$ function in non-perturbative lattice simulations. Our method is motivated by the connection between Wilsonian renormalization group and the gradient flow transformation. It does not rely on the perturbative definition of the renormalized coupling and is also valid at non-perturbative fixed points. Although our method requires an additional extrapolation compared to traditional step scaling calculations, it has several advantages which compensates for this extra step even when applied in the vicinity of the perturbative fixed point. We illustrate our approach by calculating the $\beta$ function of 2-flavor QCD and show that lattice predictions from individual lattice ensembles, even without the required continuum and finite volume extrapolations, can be very close to the result of the full analysis. Thus our method provides a non-perturbative framework and intuitive understanding into the structure of strongly coupled systems, in addition to being complementary to existing lattice determinations.

6 pages, 6 figures; v2 matching version published in Phys.Rev.D

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Cited by in corpus (17)

• Emergent strongly coupled ultraviolet fixed point in four dimensions with 8 Kähler-Dirac fermions
• Gradient flow step-scaling function for SU(3) with ten fundamental flavors
• Viscosity of pure-glue QCD from the lattice
• Lattice determinations of the strong coupling
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Infrared fixed point and anomalous dimensions in a composite Higgs model
• $\Lambda$ parameter of the SU(3) Yang-Mills theory from the continuous $\beta$ function
• Gradient flow step-scaling function for SU(3) with $N_f=8$ fundamental flavors
• Dislocations under gradient flow and their effect on the renormalized coupling
• Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
• Lattice simulations of adjoint QCD with one Dirac overlap fermion
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Tomography of the Rho meson in the QCD Instanton Vacuum: Transverse Momentum Dependent Parton Distribution Functions
• Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors
• Applications of the Perturbative Gradient Flow
• Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
• Tomography of Pions and Kaons in the QCD Vacuum: Transverse Momentum Dependent Parton Distribution Functions