Proof of the absence of multiplicative renormalizability of the Gross-Neveu model in the dimensional regularizationd=2+2ɛ

Васильев, А. Н.; Vyazovsky, M. I.

doi:10.1007/bf02634015

Cited by 20 publications

(52 citation statements)

References 17 publications

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“…Instead evanescent operators are generated in d-dimensions whose presence affects the derivation of the true renormalization group functions. This has been recognized in the earlier work of [26,27,28,29,30]. Moreover, a procedure has been developed to account for the effect of these evanescent operators, [26,27], which we will use and extend to the case of the β-function computation here.…”

Section: Preliminariesmentioning

confidence: 92%

“…We concentrate here on the formalism and give explicit details later. However, in the context of the interpretation of (2.4) in terms of generated operators without the generalized couplings g (k) then to three loops the dimensionally regularized Lagrangian which is used to determine the renormalization group functions of the strictly two dimensional theory is, [28,29,30,13],…”

Section: Preliminariesmentioning

confidence: 99%

“…Although in the case of the wave function renormalization for (2.1) the leading term of ρ (3) (g) is not required since there is no one loop correction to γ(g). In the determination of γ m (g) at four loops an error was discovered in the original evaluation of β 3 (g), [28], and in a later article [35]. Both these articles were three loop analyses and β 3 (g) had not been used or tested in the application of the projection formalism to a four loop computation.…”

Section: Preliminariesmentioning

confidence: 99%

“…Independently in [11] the Lagrangian (2.1) was renormalized without introducing an auxiliary field. Later the three loop renormalization was revisited in [28,29,30] where the generation of the evanescent operator O 3 was noted.…”

Section: Computational Technicalitiesmentioning

confidence: 99%

“…However, in the Gross-Neveu model the effect of these evanescent operators on the renormalization group functions does not become manifest until four loops. This was recognized in [28,29,30] and implemented in the construction of the four loop mass anomalous dimension in [13]. Useful in this respect was the formalism developed to account for the effect the evanescence has on the renormalization group functions given in [26,27].…”

Section: Introductionmentioning

confidence: 99%

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Four loop renormalization of the Gross-Neveu model

2016

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Abstract. We renormalize the SU (N ) Gross-Neveu model in the modified minimal subtraction (MS) scheme at four loops and determine the β-function at this order. The theory ceases to be multiplicatively renormalizable when dimensionally regularized due to the generation of evanescent 4-fermi operators. The first of these appears at three loops and we correctly take their effect into account in deriving the renormalization group functions. We use the results to provide estimates of critical exponents relevant to phase transitions in graphene.

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Section: Preliminariesmentioning

confidence: 92%

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Computational Technicalitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Four loop renormalization of the Gross-Neveu model

2016

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Anomalous dimensions of higher spin currents in large N CFTs

Hikida

Wada

2017

J. High Energ. Phys.

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Abstract:We examine anomalous dimensions of higher spin currents in the critical O(N ) scalar model and the Gross-Neveu model in arbitrary d dimensions. These two models are proposed to be dual to the type A and type B Vasiliev theories, respectively. We reproduce the known results on the anomalous dimensions to the leading order in 1/N by using conformal perturbation theory. This work can be regarded as an extension of previous work on the critical O(N ) scalars in 3 dimensions, where it was shown that the bulk computation for the masses of higher spin fields on AdS 4 can be mapped to the boundary one in conformal perturbation theory. The anomalous dimensions of the both theories agree with each other up to an overall factor depending only on d, and we discuss the coincidence for d = 3 by utilizing N = 2 supersymmetry.

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Higher-spin currents in the Gross-Neveu model at 1/n2

Manashov

Skvortsov

2017

J. High Energ. Phys.

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Abstract:We calculate the anomalous dimensions of higher-spin currents, both singlet and non-singlet, in the Gross-Neveu model at the 1/n 2 order. It was conjectured that in the critical regime this model is dual to a higher-spin gauge theory on AdS 4 . The AdS/CF T correspondence predicts that the masses of higher-spin fields correspond to the scaling dimensions of the singlet currents in the Gross-Neveu model.

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Proof of the absence of multiplicative renormalizability of the Gross-Neveu model in the dimensional regularizationd=2+2ɛ

Cited by 20 publications

References 17 publications

Four loop renormalization of the Gross-Neveu model

Four loop renormalization of the Gross-Neveu model

Anomalous dimensions of higher spin currents in large N CFTs

Higher-spin currents in the Gross-Neveu model at 1/n2

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