Physics of the Non-Abelian Coulomb Phase: Insights from Padé approximants

Thomas A. Ryttov, Robert Shrock

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Abstract

We consider a vectorial, asymptotically free SU(Nc) gauge theory with Nf fermions in a representation R having an infrared (IR) fixed point. We calculate and analyze Padé approximants to scheme-independent series expansions for physical quantities at this IR fixed point, including the anomalous dimension, γψψ,IR, to O(Δf4), and the derivative of the beta function, βIR′, to O(Δf5), where Δf is an Nf-dependent expansion variable. We consider the fundamental, adjoint, and rank-2 symmetric tensor representations. The results are applied to obtain further estimates of γψψ,IR and βIR′ for several SU(Nc) groups and representations R, and comparisons are made with lattice measurements. We apply our results to obtain new estimates of the extent of the respective non-Abelian Coulomb phases in several theories. For R=F, the limit Nc→âž and Nf→âž with Nf/Nc fixed is considered. We assess the accuracy of the scheme-independent series expansion of γψψ,IR in comparison with the exactly known expression in an N=1 supersymmetric gauge theory. It is shown that an expansion of γψψ,IR to O(Δf4) is quite accurate throughout the entire non-Abelian Coulomb phase of this supersymmetric theory.

Original languageEnglish
Article number025004
JournalPhysical Review D (Particles, Fields, Gravitation and Cosmology)
Volume97
Issue number2
Number of pages24
ISSN0556-2821
DOIs
Publication statusPublished - 15. Jan 2018

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series expansion
physics
gauge theory
expansion
estimates
fermions
tensors

Keywords

  • hep-th
  • hep-lat
  • hep-ph

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title = "Physics of the Non-Abelian Coulomb Phase: Insights from Pad{\'e} approximants",
abstract = "We consider a vectorial, asymptotically free SU(Nc) gauge theory with Nf fermions in a representation R having an infrared (IR) fixed point. We calculate and analyze Pad{\'e} approximants to scheme-independent series expansions for physical quantities at this IR fixed point, including the anomalous dimension, γψψ,IR, to O(Δf4), and the derivative of the beta function, βIR′, to O(Δf5), where Δf is an Nf-dependent expansion variable. We consider the fundamental, adjoint, and rank-2 symmetric tensor representations. The results are applied to obtain further estimates of γψψ,IR and βIR′ for several SU(Nc) groups and representations R, and comparisons are made with lattice measurements. We apply our results to obtain new estimates of the extent of the respective non-Abelian Coulomb phases in several theories. For R=F, the limit Nc→{\^a}ž and Nf→{\^a}ž with Nf/Nc fixed is considered. We assess the accuracy of the scheme-independent series expansion of γψψ,IR in comparison with the exactly known expression in an N=1 supersymmetric gauge theory. It is shown that an expansion of γψψ,IR to O(Δf4) is quite accurate throughout the entire non-Abelian Coulomb phase of this supersymmetric theory.",
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doi = "10.1103/PhysRevD.97.025004",
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Physics of the Non-Abelian Coulomb Phase : Insights from Padé approximants. / Ryttov, Thomas A.; Shrock, Robert.

In: Physical Review D (Particles, Fields, Gravitation and Cosmology), Vol. 97, No. 2, 025004, 15.01.2018.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Physics of the Non-Abelian Coulomb Phase

T2 - Insights from Padé approximants

AU - Ryttov, Thomas A.

AU - Shrock, Robert

N1 - 28 pages, 3 figures

PY - 2018/1/15

Y1 - 2018/1/15

N2 - We consider a vectorial, asymptotically free SU(Nc) gauge theory with Nf fermions in a representation R having an infrared (IR) fixed point. We calculate and analyze Padé approximants to scheme-independent series expansions for physical quantities at this IR fixed point, including the anomalous dimension, γψψ,IR, to O(Δf4), and the derivative of the beta function, βIR′, to O(Δf5), where Δf is an Nf-dependent expansion variable. We consider the fundamental, adjoint, and rank-2 symmetric tensor representations. The results are applied to obtain further estimates of γψψ,IR and βIR′ for several SU(Nc) groups and representations R, and comparisons are made with lattice measurements. We apply our results to obtain new estimates of the extent of the respective non-Abelian Coulomb phases in several theories. For R=F, the limit Nc→âž and Nf→âž with Nf/Nc fixed is considered. We assess the accuracy of the scheme-independent series expansion of γψψ,IR in comparison with the exactly known expression in an N=1 supersymmetric gauge theory. It is shown that an expansion of γψψ,IR to O(Δf4) is quite accurate throughout the entire non-Abelian Coulomb phase of this supersymmetric theory.

AB - We consider a vectorial, asymptotically free SU(Nc) gauge theory with Nf fermions in a representation R having an infrared (IR) fixed point. We calculate and analyze Padé approximants to scheme-independent series expansions for physical quantities at this IR fixed point, including the anomalous dimension, γψψ,IR, to O(Δf4), and the derivative of the beta function, βIR′, to O(Δf5), where Δf is an Nf-dependent expansion variable. We consider the fundamental, adjoint, and rank-2 symmetric tensor representations. The results are applied to obtain further estimates of γψψ,IR and βIR′ for several SU(Nc) groups and representations R, and comparisons are made with lattice measurements. We apply our results to obtain new estimates of the extent of the respective non-Abelian Coulomb phases in several theories. For R=F, the limit Nc→âž and Nf→âž with Nf/Nc fixed is considered. We assess the accuracy of the scheme-independent series expansion of γψψ,IR in comparison with the exactly known expression in an N=1 supersymmetric gauge theory. It is shown that an expansion of γψψ,IR to O(Δf4) is quite accurate throughout the entire non-Abelian Coulomb phase of this supersymmetric theory.

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U2 - 10.1103/PhysRevD.97.025004

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