Anomaly in the conformal spinor current

Inagaki, H.

doi:10.1007/bf02785154

Cited by 4 publications

(2 citation statements)

References 6 publications

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“…Let [ Ĵα α] be the supercurrent, renormalized so that its expectation value is finite and is exactly equal to what one would get by putting into Ĵα α the external fields alone 7 . Note that [ Ĵα α] is the supercurrent that contains the energy-momentum tensor in its θ θ component .…”

Section: A a Manifestly Supersymmetric Derivationmentioning

confidence: 99%

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Clarifying some remaining questions in the anomaly puzzle

Huang

Parker

2011

Eur. Phys. J. C

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We discuss several points that may help to clarify some questions that remain about the anomaly puzzle in supersymmetric theories. In particular, we consider a general N = 1 supersymmetric Yang-Mills theory. The anomaly puzzle concerns the question of whether there is a consistent way to put the R-current and the stress tensor in a single supercurrent, even though in the classical theory they are in the same supermultiplet. As is well known, the classically conserved supercurrent bifurcates into two supercurrents having different anomalies in the quantum regime. The most interesting result we obtain is an explicit expression for the lowest component of one of the two supercurrents in 4-dimensional spacetime, namely the supercurrent that has the energy-momentum tensor as one of its components. This expression for the lowest component is an energy-dependent linear combination of two chiral currents, which itself does not correspond to a classically conserved chiral current. The lowest component of the other supercurrent, namely, the R-current, satisfies the Adler-Bardeen theorem. The lowest component of the first supercurrent has an anomaly that we show is consistent with the anomaly of the trace of the energy-momentum tensor. Therefore, we conclude that there is no consistent way to put the R-current and the stress tensor in a single supercurrent in the quantized theory. We also discuss and try to clarify some technical points in the derivations of the two-supercurrents in the literature. These latter points concern the significance of infrared contributions to the NSVZ β-function and the role of the equations of motion in deriving the two supercurrents.

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Section: A a Manifestly Supersymmetric Derivationmentioning

confidence: 99%

“…This chiral anomaly is proportional to the topological invariant, F µν Fµν , and can be expressed in an operator equation. One can try to generalize the operator equation of this anomaly of the R-symmetry to a supersymmetric form involving J µ [2][3][4][5][6][7]. However, this attempt led to an apparent contradiction.…”

Section: Introductionmentioning

confidence: 99%

Clarifying some remaining questions in the anomaly puzzle

Huang

Parker

2011

Eur. Phys. J. C

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Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories

Ensign

Mahanthappa

1987

Phys. Rev. D

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We construct the supercurrent and a supersymmetric current which satisfies the Adler-Bardeen theorem in supersymmetric Yang-Miils theory coupled to non-self-interacting chiral matter. Using the formulatiori recently developed by Grisaru, Milewski, and Zanon, supersymmetry and gauge invariance are maintained with supersymmetric background-field theory and regularization by dimensional reduction. We verify the finiteness of the supercurrent to one loop, and the Adler-Bardeen theorem to two loops by explicit calculations in the minimal-subtraction scheme. We then demonstrate the subtraction-scheme independence of the one-loop Adler-Bardeen anomaly and prove the existence of a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory. Soon after, ones' "solved" the consistency problem in an apparently simple way which also provided an allorders derivation of the / 3 function. His arguments were the following. The component G of the anomaly superfield which contains the axial anomaly has the form If the AB theorem is assumed, the anomalous divergence of the axial-vector current is equal to its one-loop value:Since it is the first component of the supercurrent, the anomalous divergence of j: should also be related to the /3 function and the anomaly superfield component G by Given these assumptions, not only are Eq. (1.2), which represents the AB theorem, and Eq. (1.31, the supercurrent equation, consistent, but they can also be solved for the all-orders /3 function. Amazingly, this procedure gives the correct two-loop value for the /3 function in pure supersymmetric Yang-Mills theory. Jones and

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Superconformal constraints for QCD conformal anomalies

Belitsky

Müller²

2002

Phys. Rev. D

271

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Anomalous superconformal Ward identities and commutator algebra in N = 1 super-Yang-Mills theory give rise to constraints between the QCD special conformal anomalies of conformal composite operators. We evaluate the superconformal anomalies that appear in the product of renormalized conformal operators and the trace anomaly in the supersymmetric spinor current and check the constraints at one-loop order. In this way we prove the universality of QCD conformal anomalies, which define the non-diagonal part of the anomalous dimension matrix responsible for scaling violations of exclusive QCD amplitudes at the next-to-leading order.Comment: 30 pages, 2 figures, LaTe

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Anomaly in the conformal spinor current

Cited by 4 publications

References 6 publications

Clarifying some remaining questions in the anomaly puzzle

Clarifying some remaining questions in the anomaly puzzle

Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories

Superconformal constraints for QCD conformal anomalies

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