Point-splitting derivation of anomalous divergence for the spinor current

Inagaki, H.

doi:10.1016/0370-2693(78)90198-3

Cited by 18 publications

(5 citation statements)

References 7 publications

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“…3. At this point, it is interesting to note that the above expression reproduces the gamma-trace anomaly (superconformal anomaly) [62][63][64][65][66][67][68][69][70] γ µ S µR (x) = −g/(4π) 2 C 2 (G)3σ µν ψ a (x)F a νµ (x) + O(g 3 ) at least in the one-loop order, because γ µ σ ρσ γ µ = 0 for D = 4 and flowed fields simply reduce to the corresponding un-flowed fields in the t → 0 limit in the lowest order of perturbation theory. This is reassuring, because the properly normalized conserved supercurrent must possess this gamma-trace anomaly.…”

Section: Introductionmentioning

confidence: 87%

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4D N = 1 SYM supercurrent on the lattice in terms of the gradient flow

Hieda¹,

Kasai²,

Makino³

et al. 2018

EPJ Web Conf.

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The gradient flow [1][2][3][4][5] gives rise to a versatile method to construct renormalized composite operators in a regularization-independent manner. By adopting this method, the authors of Refs. [6-9] obtained the expression of Noether currents on the lattice in the cases where the associated symmetries are broken by lattice regularization. We apply the same method to the Noether current associated with supersymmetry, i.e., the supercurrent. We consider the 4D N = 1 super Yang-Mills theory and calculate the renormalized supercurrent in the one-loop level in the Wess-Zumino gauge. We then re-express this supercurrent in terms of the flowed gauge and flowed gaugino fields [10].

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Section: Introductionmentioning

confidence: 87%

“…(3.37) reproduces the superconformal anomaly (Refs. [62][63][64][65][66][67][68][69][70]), γ µ S µR (x) = − β(g) g 2 {σ µν ψ a F a µν } R (x), (B1)…”

Section: B Two-loop Order Improvement Through the Superconformal Anomalymentioning

confidence: 99%

4D N = 1 SYM supercurrent on the lattice in terms of the gradient flow

Hieda¹,

Kasai²,

Makino³

et al. 2018

EPJ Web Conf.

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show abstract

“…On-shell conditions are applied before Feynman parameter integrations. Fermionic and bosonic propagators are modified in this method introducing a regularization parameter κ, Using Point-Splitting regularization, in [77] was shown an anomaly for spinor current which, however, could be removed by a redefinition of the gauge invariant conserved current keeping the spin-3=2 constraint satisfied.…”

Section: A Digression On the Results Of The Literaturementioning

confidence: 99%

Supercurrent anomaly and gauge invariance in the N=1 supersymmetric Yang-Mills theory

et al. 2018

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We analyze Feynman diagram calculational issues related to the quantum breaking of supercurrent conservation in a supersymmetric non-Abelian Yang-Mills theory. For the sake of simplicity, we take a zero mass gauge field multiplet interacting with a massless Majorana spin-1=2 field in the adjoint representation of SUð2Þ. We shed light on a long-standing controversy regarding the perturbative evaluation of the supercurrent anomaly in connection with gauge and superconformal symmetry in different frameworks. We find that only superconformal symmetry is unambiguously broken using an invariant four dimensional regularization and compare with the triangle AVV anomaly. Subtleties related to momentum routing invariance in the loops of diagrams and Clifford algebra evaluation inside divergent integrals are also discussed in connection with finite and undetermined quantities in Feynman amplitudes.

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“…(3.4) and the term with the coefficient c does not affect the conservation law as we already explained. We note that, with our definition of the energy-momentum tensor (3.4), the trace anomaly [52,53,54,55] and the gamma-trace anomaly (superconformal anomaly) [56,57,58,59,60,61,62,63,64] are related by 10…”

Section: A Lattice Energy-momentum Tensor and Its Conservation Lawmentioning

confidence: 99%

Ferrara–Zumino supermultiplet and the energy–momentum tensor in the lattice formulation of 4D SYM

Suzuki¹

2013

Nuclear Physics B

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In a recent paper, arXiv:1209.2473 [1], we presented a possible definition of the energy-momentum tensor in the lattice formulation of the four-dimensional N = 1 supersymmetric Yang-Mills theory, that is conserved in the quantum continuum limit. In the present Letter, we propose a quite similar but somewhat different definition of the energy-momentum tensor (that is also conserved in the continuum limit) which is superior in several aspects: In the continuum limit, the origin of the energy automatically becomes consistent with the supersymmetry and the number of renormalization constants that require a (non-perturbative) determination is reduced to two from four, the number of renormalization constants appearing in the construction in Ref. [1].

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Point-splitting derivation of anomalous divergence for the spinor current

Cited by 18 publications

References 7 publications

4D N = 1 SYM supercurrent on the lattice in terms of the gradient flow

4D N = 1 SYM supercurrent on the lattice in terms of the gradient flow

Supercurrent anomaly and gauge invariance in the N=1 supersymmetric Yang-Mills theory

Ferrara–Zumino supermultiplet and the energy–momentum tensor in the lattice formulation of 4D SYM

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