Pre-regularization for supersymmetry

Elias, V.; McKeon, Gerry; Phillips, S.B.; Mann, Robert B.

doi:10.1016/0370-2693(83)90111-9

Cited by 19 publications

(14 citation statements)

References 18 publications

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“…It is immediate from above that the Kronecker delta signs a discontinuity in the dimensionality ω. The authors use these results to back up an integer dimensional regularization called Preregularization where the freedom of momentum routing in the loops is chosen to cancel out some surface terms thus preserving Ward identities in chiral anomalies or supersymmetry [34][35][36]. A relevant question, given that shifts of integration variables are regularization dependent, would be to verify whether the argument could be turned the other way around, namely to exploit the consequences of momentum routing invariance over regularization schemes.…”

Section: A General View Of Regularization Dependent Integralsmentioning

confidence: 99%

(Un)determined finite regularization-dependent quantum corrections: The Higgs boson decay into two photons and the two-photon scattering examples

et al. 2013

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We investigate the appearance of arbitrary, regularization dependent parameters introduced by divergent integrals in two a priori finite but superficially divergent amplitudes: the Higgs decay into two photons and the two photon scattering. We use a general parametrization of ultraviolet divergences which makes explicit such ambiguities. Thus we separate in a consistent way using Implicit Regularization the divergent, finite and regularization dependent parts of the amplitudes which in turn are written as surface terms. We find that, although finite, these amplitudes are ambiguous before the imposition of physical conditions namely momentum routing invariance in the loops of Feynman diagrams. In the examples we study momentum routing invariance turns out to be equivalent to gauge invariance. We also discuss the results obtained by different regularizations and show how they can be reproduced within our framework allowing for a clear view on the origin of regularization ambiguities.

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Section: A General View Of Regularization Dependent Integralsmentioning

confidence: 99%

(Un)determined finite regularization-dependent quantum corrections: The Higgs boson decay into two photons and the two-photon scattering examples

et al. 2013

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“…In the early eighties, motivated by the construction of a framework applicable to models which are incompatible with dimensional continuation on the space-time dimension (for instance supersymmetric, chiral and topological quantum field theories), Elias, McKeon, Mann and collaborators [2] brought back the problem on loop momentum routing ambiguities. The latter stem from shift of integration variable surface terms which appear in the integer dimension but not in dimensionally continued space-times.…”

Section: Introductionmentioning

confidence: 99%

Momentum routing invariance in Feynman diagrams and quantum symmetry breakings

et al. 2012

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We illustrate with examples that quantum symmetry breakings in perturbation theory are connected to breakdown of momentum routing invariance (MRI) in the loops of a Feynman diagram.We show that MRI is a necessary and sufficient condition to preserve abelian gauge symmetry at arbitrary loop order. We adopt the implicit regularization framework in which surface terms that are directly connected to momentum routing can be constructed to arbitrary loop order. The interplay between momentum routing invariance, surface terms and anomalies is discussed. We also illustrate that MRI is important to preserve supersymmetry. For theories with poor symmetry content, such as scalar field theories, MRI is shown to be important in the calculation of renormalization group functions.

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“…Any attempt to define it in n dimensions must be done in 'Present address: Department of Applied Mathematics, University of Western Ontario, London, Ont., Canada N6A 5B9. a somewhat ad hoc manner s o as to reproduce the chiral anomaly (7). W e seek to develop procedures for ensuring that radiative corrections to physical processes respect the Ward-TakahashiSlavnov-Taylor (WTST) identities (4) that follow from symmetries of the initial Lagrangian, a method that does not entail a redefinition of the theory through inclusion of a regulating parameter (e.g., the dimerision of space-time or the mass of a regulator field).…”

Section: Introductionmentioning

confidence: 99%

“…W e seek to develop procedures for ensuring that radiative corrections to physical processes respect the Ward-TakahashiSlavnov-Taylor (WTST) identities (4) that follow from symmetries of the initial Lagrangian, a method that does not entail a redefinition of the theory through inclusion of a regulating parameter (e.g., the dimerision of space-time or the mass of a regulator field). Earlier work (8) has shown how the surface term associated with shifting the variable of integration in a more-than-logarithmically divergent Feynman integral can permit calculation of radiative corrections in such a way that WTST identities are preserved, regardless of how divergent integrals are parameterized, without having to redefine the theory.…”

Section: Introductionmentioning

confidence: 99%

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Preregularization

Elias¹,

Mann²,

Chowdhury³

et al. 1985

Can. J. Phys.

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We describe and investigate the applicability of a recently proposed preregularization procedure in which arbitrary shift-of-integration-variable surface terms (in four dimensions) arising from loop-mementum ambiguities are constrained to absorb any contributions to unrenormalized Feynman amplitudes that violate Ward-Takahashi-Slavnov-Taylor (WTST) identities appropriate to the theory under consideration. Anomalies in WTST identities are shown to be the result of having insufficient arbitrariness in the loop momenta to accommodate the full set of Lagrangian symmetries. We demonstrate the utility of our procedure by analyzing the chiral anomaly in even dimensions, the supercurrent anomaly in N = 1 super Yang-Mills theory, and by calculations in quantum electrodynamics and Yang-Mills theory. We argue that the preregularization procedure should be particularly well suited to supersymmetric theories as a regularization-independent means of upholding super-WTST identities.Nous Ctudions l'applicabilitk d'une prockdure de preregularisation proposke rkcemment, dans laquelle des termes de surface (en quatre dimensions) dus a des decalages de variables d'intkgration provenant d'ambiguites boucle-impulsion sont contraints 5 absorber toutes les contributions aux amplitudes de Feynman non renormalisees qui violent les identitks Ward-TakahashiSlavnov-Taylor (WTST) approprikes a la thkorie considkree. On montre que les anomalies dans les identitks WTST sont le rksultat d'une insuffisance d'arbitraire, dans les boucles-impulsions, qui empkche d'accommoder au complet l'ensemble des symCtries du lagrangien. Nous dkmontrons 1'utilitC de notre prockdure en analysant l'anomalie chirale en nombre pair de dimensions, l'anomalie de supercourant en thkorie super-Yang-Mills N = 1, ainsi que par des calculs en EDQ et en thtorie Yang-Mills. Nous indiquons ainsi que le prockdure de prC-regularisation devrait ktre particulikrement bien adaptCe aux thCories supersymCtriques, comme support independant de la rkgularisation des identitts super-WTST.[Traduit par le journal]Can.

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Pre-regularization for supersymmetry

Cited by 19 publications

References 18 publications

(Un)determined finite regularization-dependent quantum corrections: The Higgs boson decay into two photons and the two-photon scattering examples

(Un)determined finite regularization-dependent quantum corrections: The Higgs boson decay into two photons and the two-photon scattering examples

Momentum routing invariance in Feynman diagrams and quantum symmetry breakings

Preregularization

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