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 TMF, 2004, Volume 140, Number 1, Pages 53–77 (Mi tmf83)

Anomaly Problem in the $N=1$ Supersymmetric Electrodynamics as a Consequence of the Inconsistency of the Dimensional Reduction Method

K. V. Stepanyantz

M. V. Lomonosov Moscow State University

Abstract: We compare the calculation of the two-loop $\beta$-function in the $N=1$ supersymmetric electrodynamics regularized via higher derivatives and via dimensional reduction. We show that the renormalized effective action is the same for both regularizations. But in the method of higher derivatives, unlike in the dimensional reduction, the $\beta$-function defined as the derivative of the renormalized coupling constant with respect $\ln\mu$ turns out to be purely one-loop. The anomaly problem therefore does not occur in this regularization, because in the method of higher derivatives, the diagrams with counterterm insertions make a nonzero contribution, which is evaluated exactly in all orders of the perturbation theory. When dimensional reduction is used, this contribution is zero. We argue that this result is a consequence of the mathematical inconsistency of the dimensional reduction method and that just this inconsistency leads to the anomaly problem.

Keywords: supersymmetry, regularization, higher covariant derivatives, dimensional reduction

DOI: https://doi.org/10.4213/tmf83

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English version:
Theoretical and Mathematical Physics, 2004, 140:1, 939–957

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Revised: 06.06.2003

Citation: K. V. Stepanyantz, “Anomaly Problem in the $N=1$ Supersymmetric Electrodynamics as a Consequence of the Inconsistency of the Dimensional Reduction Method”, TMF, 140:1 (2004), 53–77; Theoret. and Math. Phys., 140:1 (2004), 939–957

Citation in format AMSBIB
\Bibitem{Ste04} \by K.~V.~Stepanyantz \paper Anomaly Problem in the $N=1$ Supersymmetric Electrodynamics as a~Consequence of the Inconsistency of the Dimensional Reduction Method \jour TMF \yr 2004 \vol 140 \issue 1 \pages 53--77 \mathnet{http://mi.mathnet.ru/tmf83} \crossref{https://doi.org/10.4213/tmf83} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2004TMP...140..939S} \transl \jour Theoret. and Math. Phys. \yr 2004 \vol 140 \issue 1 \pages 939--957 \crossref{https://doi.org/10.1023/B:TAMP.0000033031.20411.2b} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000223573800005} 

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• https://doi.org/10.4213/tmf83
• http://mi.mathnet.ru/eng/tmf/v140/i1/p53

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. A. Soloshenko, K. V. Stepanyantz, “Three-Loop $\beta$-Function of $N=1$ Supersymmetric Electrodynamics Regularized by Higher Derivatives”, Theoret. and Math. Phys., 140:3 (2004), 1264–1282
2. K. V. Stepanyantz, “Investigating the anomaly puzzle in $N=1$ supersymmetric electrodynamics”, Theoret. and Math. Phys., 142:1 (2005), 29–47
3. K. V. Stepanyantz, “Contribution of matter fields to the Gell-Mann–Low function for the $N=1$ supersymmetric Yang–Mills theory regularized by higher covariant derivatives”, Theoret. and Math. Phys., 150:3 (2007), 377–392
4. A. B. Pimenov, K. V. Stepanyantz, “Two-loop Gell-Mann–Low function of the $N=1$ supersymmetric Yang–Mills theory regularized by higher covariant derivatives”, Theoret. and Math. Phys., 155:3 (2008), 848–861
5. Pimenov, AB, “REGULARIZATION BY HIGHER DERIVATIVES AND QUANTUM CORRECTION FOR N=1 SUPERSYMMETRIC THEORIES”, Russian Physics Journal, 51:5 (2008), 444
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