Dimensional regularization and supersymmetry

Avdeev, L.V.; Vladimirov, A. A.

doi:10.1016/0550-3213(83)90437-6

Cited by 148 publications

(84 citation statements)

References 17 publications

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“…This regularization is consistent at low orders of perturbation theory as long as antisymmetric Levi-Civita tensors are not present, and manifestly preserves supersymmetry. (See the discussion in [35]. )…”

Section: Diagrams With E Iϕmentioning

confidence: 99%

Operators with Large R-Charge in N=4 Yang–Mills Theory

Gross¹,

Mikhailov²,

Roiban³

2002

Annals of Physics

167

264

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It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N = 4 supersymmetric Yang-Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a particular case of the AdS/CFT correspondence, it is a priori a strong/weak coupling duality. However, the predictions for the anomalous dimensions which follow from this particular limit are analytic functions of the 't Hooft coupling constant λ and have a well defined expansion in the weak coupling regime. This allows one to conjecture that the correspondence between the strings on the plane wave background and the Yang-Mills theory works at the level of perturbative expansions.In our paper we perform perturbative computations in the Yang-Mills theory that confirm this conjecture. We calculate the anomalous dimension of the operator corresponding to the elementary string excitation. We verify at the two loop level that the anomalous dimension has a finite limit when the R charge J → ∞ keeping λ/J 2 finite. We conjecture that this is true at higher orders of perturbation theory. We show, by summing an infinite subset of Feynman diagrams, under the above assumption, that the anomalous dimensions arising from the Yang-Mills perturbation theory are in agreement with the anomalous dimensions following from the string worldsheet sigma-model.

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Section: Diagrams With E Iϕmentioning

confidence: 99%

Operators with Large R-Charge in N=4 Yang–Mills Theory

Gross¹,

Mikhailov²,

Roiban³

2002

Annals of Physics

167

264

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“…One can easily verify that the sum 26) JHEP05 (2016)014 which is obtained after the gauge fixing procedure, is invariant under the background gauge transformations (2.11), under which f and ghost superfields should be transformed as…”

Section: Adjmentioning

confidence: 99%

“…This regularization is mathematically consistent unlike the dimensional reduction [24]. (Removing the inconsistencies of the dimensional reduction leads to the loss of the explicit supersymmetry [25], which can be in this case broken by higher order quantum corrections [26][27][28].) The higher covariant derivative regularization can be formulated in the explicitly N = 1 supersymmetric way [29,30], so that it does not break supersymmetry.…”

Section: Jhep05(2016)014mentioning

confidence: 99%

One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization

Aleshin

Kazantsev

Skoptsov

et al. 2016

J. High Energ. Phys.

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We consider a general non-Abelian renormalizable N = 1 supersymmetric gauge theory, regularized by higher covariant derivatives without breaking the BRST invariance, and calculate one-loop divergences for a general form of higher derivative regulator and of the gauge fixing term. It is demonstrated that the momentum integrals giving the one-loop β-function are integrals of double total derivatives independently of a particular choice of the higher derivative term. Evaluating them we reproduce the well-known result for the one-loop β-function. Also we find that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in the considered approximation.

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“…However, it is well known that DRED is not mathematically consistent [20]. Its inconsistency leads to the loss of explicit SUSY [21], which will be broken by quantum corrections in higher loops [22,23]. Nevertheless, a recent analytical calculation [24] demonstrates that the DRED regularization and the DR scheme are working in the N = 4 SYM theory up to the four-loop approximation and give the vanishing result for its β-function.…”

Section: Introductionmentioning

confidence: 99%

NSVZ scheme with the higher derivative regularization for SQED

2013

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The exact NSVZ relation between a β-function of N = 1 SQED and an anomalous dimension of the matter superfields is studied within the Slavnov higher derivative regularization approach. It is shown that if the renormalization group functions are defined in terms of the bare coupling constant, this relation is always valid. In the renormalized theory the NSVZ relation is obtained in the momentum subtraction scheme supplemented by a special finite renormalization. Unlike the dimensional reduction, the higher derivative regularization allows to fix this finite renormalization. This is made by imposing the conditions Z 3 (α, µ = Λ) = 1 and Z(α, µ = Λ) = 1 on the renormalization constants of N = 1 SQED, where Λ is a parameter in the higher derivative term. The results are verified by the explicit three-loop calculation. In this approximation we relate the DR scheme and the NSVZ scheme defined within the higher derivative approach by the finite renormalization.

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Dimensional regularization and supersymmetry

Cited by 148 publications

References 17 publications

Operators with Large R-Charge in N=4 Yang–Mills Theory

Operators with Large R-Charge in N=4 Yang–Mills Theory

One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization

NSVZ scheme with the higher derivative regularization for SQED

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