Critical dimensions of composite operators in the nonlinear σ-model

Derkachov, S. E.; Manashov, A. N.

doi:10.1007/bf02557145

Cited by 13 publications

(25 citation statements)

References 23 publications

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“…The more widely used method for this is the method of self-consistency equations, which is based on the direct solution of the Schwinger-Dyson (SD) equations, [12,14,22,28]. Another approach has been developed recently in [20,21] and will be briefly discussed below in the context of QCD.…”

Section: Methodsmentioning

confidence: 99%

“…The convenience of the RG method from the computational point of view consists of the possibility of calculating critical exponents via the renormalizaton constants given in (2.5). To retain this calculational advantage, following the lines of [14,20,21], we restore the multiplicative renormalizability of the model in question by attaching two additional charges, u and v, to the last two terms of the action (3.1). Namely, we consider the model with the action…”

Section: Extended Modelmentioning

confidence: 99%

“…It is worth noting that our detailed calculation relies on the novel method of [20,21] for the computation of critical exponents in 1/N expansion. In comparison with the standard technique [12] based on the direct solution of the Schwinger-Dyson (SD) equations the latter approach allows us to express the critical exponents through the corresponding renormalization constants whose explicit form is very similar to those computed using dimensional regularization.…”

Section: Introductionmentioning

confidence: 99%

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Computation of quark mass anomalous dimension at O(1/N2) in quantum chromodynamics

Ciuchini¹,

Derkachov²,

Gracey³

et al. 2000

Nuclear Physics B

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Abstract. We present the formalism to calculate d-dimensional critical exponents in QCD in the large N f expansion where N f is the number of quark flavours. It relies in part on demonstrating that at the d-dimensional fixed point of QCD the critical theory is equivalent to a non-abelian version of the Thirring model. We describe the techniques used to compute critical two and three loop Feynman diagrams and as an application determine the quark wave function, η, and mass renormalization critical exponents at O(1/N 2 f ) in d-dimensions. Their values when expressed in relation to four dimensional perturbation theory are in exact agreement with the known four loop MS results. Moreover, new coefficients in these renormalization group functions are determined to six loops and O(1/N 2 f ). The computation of the exponents in the Schwinger Dyson approach is also provided and an expression for η in arbitrary covariant gauge is given. *

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Section: Methodsmentioning

confidence: 99%

Section: Extended Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computation of quark mass anomalous dimension at O(1/N2) in quantum chromodynamics

Ciuchini¹,

Derkachov²,

Gracey³

et al. 2000

Nuclear Physics B

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“…An interested reader can find detailed discussions in Refs. [24,27]. Thus at the order 1/n 2 one can neglect mixing and calculate only the diagonal matrix elements.…”

Section: Correction Exponents At 1/nmentioning

confidence: 99%

“…Therefore we use a different method developed in [21][22][23]. A detailed description of the method can be found in [23,24] and an application to the GN model in [25].…”

Section: Introductionmentioning

confidence: 99%

Correction exponents in the Gross–Neveu–Yukawa model at $$1/N^2$$ 1 / N 2

Manashov

Strohmaier

2018

Eur. Phys. J. C

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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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Critical dimensions of composite operators in the nonlinear σ-model

Cited by 13 publications

References 23 publications

Computation of quark mass anomalous dimension at O(1/N2) in quantum chromodynamics

Computation of quark mass anomalous dimension at O(1/N2) in quantum chromodynamics

Correction exponents in the Gross–Neveu–Yukawa model at $$1/N^2$$ 1 / N 2

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

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