Critical exponents to order ϵ<sup>3</sup>for ϕ<sup>3</sup>models of critical phenomena in 6-ϵ dimensions

Bonfim, O. F. de Alcantara; Kirkham, Jackie; McKane, Alan J.

doi:10.1088/0305-4470/13/7/006

Cited by 113 publications

(54 citation statements)

References 22 publications

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“…This result is consistent with the perturbation results (see, for example, [21][22][23]). The conformal method developed in [1] was not applicable to this theory since they crucially used the conditions that γ 1 = O( 2 ) and γ n>1 = O( ).…”

Section: Jhep07(2016)107supporting

confidence: 92%

Classical equation of motion and anomalous dimensions at leading order

Nii

2016

J. High Energ. Phys.

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Motivated by a recent paper by Rychkov-Tan [1], we calculate the anomalous dimensions of the composite operators at the leading order in various models including a φ 3 -theory in (6 − ) dimensions. The method presented here relies only on the classical equation of motion and the conformal symmetry. In case that only the leading expressions of the critical exponents are of interest, it is sufficient to reduce the multiplet recombination discussed in [1] to the classical equation of motion. We claim that in many cases the use of the classical equations of motion and the CFT constraint on two-and three-point functions completely determine the leading behavior of the anomalous dimensions at the Wilson-Fisher fixed point without any input of the Feynman diagrammatic calculation. The method developed here is closely related to the one presented in [1] but based on a more perturbative point of view.

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Section: Jhep07(2016)107supporting

confidence: 92%

Classical equation of motion and anomalous dimensions at leading order

Nii

2016

J. High Energ. Phys.

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“…[23,24], although our couplings are more general than those articles. However, one can always make contact with the results of refs.…”

Section: Jhep01(2016)174 3 Three-loop Resultsmentioning

confidence: 86%

“…However, one can always make contact with the results of refs. [23,24] by setting g ijk = gd ijk where g was the coupling constant and d ijk was a group valued object which is completely symmetric in its indices like g ijk . For example, if φ i took values in the adjoint representation of SU(N c ) then d ijk would be the corresponding totally symmetric rank 3 colour tensor of that group.…”

Section: Jhep01(2016)174 3 Three-loop Resultsmentioning

confidence: 99%

“…[23,24,29] to three loops and the wave function and coupling constant renormalisation constants were deduced from the divergences in the 2-and 3-point functions. For the latter the pole structure was determined by exploiting specific properties of the six dimensional spacetime.…”

Section: Jhep01(2016)174 3 Three-loop Resultsmentioning

confidence: 99%

“…(3.10), (3.11) explicitly and independently; and we have checked that we reproduce the wave function and β-function results of refs. [22] and [23,24] (in the latter case, after we specialize to the corresponding restriction on the group theory structure used there). Although in ref.…”

Section: Jhep01(2016)174mentioning

confidence: 99%

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