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Title: Continuous renormalization group β function from lattice simulations

Abstract

We present a real-space renormalization group transformation with continuous scale change to calculate the continuous renormalization group β function in nonperturbative 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 nonperturbative 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 β 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 nonperturbative framework and intuitive understanding into the structure of strongly coupled systems, in addition to being complementary to existing lattice determinations.

Authors:
ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
OSTI Identifier:
1601075
Alternate Identifier(s):
OSTI ID: 1607672; OSTI ID: 1765354
Grant/Contract Number:  
SC0010005; ACI-1532235; ACI-1532236; ACI-1548562; AC02-05CH11231
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; gauge theories; lattice field theory; renormalization group

Citation Formats

Hasenfratz, Anna, and Witzel, Oliver. Continuous renormalization group β function from lattice simulations. United States: N. p., 2020. Web. doi:10.1103/PhysRevD.101.034514.
Hasenfratz, Anna, & Witzel, Oliver. Continuous renormalization group β function from lattice simulations. United States. doi:https://doi.org/10.1103/PhysRevD.101.034514
Hasenfratz, Anna, and Witzel, Oliver. Sat . "Continuous renormalization group β function from lattice simulations". United States. doi:https://doi.org/10.1103/PhysRevD.101.034514.
@article{osti_1601075,
title = {Continuous renormalization group β function from lattice simulations},
author = {Hasenfratz, Anna and Witzel, Oliver},
abstractNote = {We present a real-space renormalization group transformation with continuous scale change to calculate the continuous renormalization group β function in nonperturbative 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 nonperturbative 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 β 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 nonperturbative framework and intuitive understanding into the structure of strongly coupled systems, in addition to being complementary to existing lattice determinations.},
doi = {10.1103/PhysRevD.101.034514},
journal = {Physical Review D},
number = 3,
volume = 101,
place = {United States},
year = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1103/PhysRevD.101.034514

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Cited by: 1 work
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