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 TMF, 2004, Volume 140, Number 3, Pages 437–459 (Mi tmf106)

Three-Loop $\beta$-Function of $N=1$ Supersymmetric Electrodynamics Regularized by Higher Derivatives

A. A. Soloshenko, K. V. Stepanyantz

M. V. Lomonosov Moscow State University

Abstract: We calculate three-loop corrections to the effective action for $N=1$ supersymmetric electrodynamics regularized by higher derivatives. Using the obtained results, we investigate the anomaly problem in the considered model.

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

DOI: https://doi.org/10.4213/tmf106

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English version:
Theoretical and Mathematical Physics, 2004, 140:3, 1264–1282

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Revised: 12.01.2004

Citation: A. A. Soloshenko, K. V. Stepanyantz, “Three-Loop $\beta$-Function of $N=1$ Supersymmetric Electrodynamics Regularized by Higher Derivatives”, TMF, 140:3 (2004), 437–459; Theoret. and Math. Phys., 140:3 (2004), 1264–1282

Citation in format AMSBIB
\Bibitem{SolSte04} \by A.~A.~Soloshenko, K.~V.~Stepanyantz \paper Three-Loop $\beta$-Function of $N=1$ Supersymmetric Electrodynamics Regularized by Higher Derivatives \jour TMF \yr 2004 \vol 140 \issue 3 \pages 437--459 \mathnet{http://mi.mathnet.ru/tmf106} \crossref{https://doi.org/10.4213/tmf106} \zmath{https://zbmath.org/?q=an:1178.81252} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2004TMP...140.1264S} \transl \jour Theoret. and Math. Phys. \yr 2004 \vol 140 \issue 3 \pages 1264--1282 \crossref{https://doi.org/10.1023/B:TAMP.0000039832.82367.50} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000224901800007} 

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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. K. V. Stepanyantz, “Investigating the anomaly puzzle in $N=1$ supersymmetric electrodynamics”, Theoret. and Math. Phys., 142:1 (2005), 29–47
2. A. B. Pimenov, K. V. Stepanyantz, “Four-loop verification of an algorithm for summing Feynman diagrams in the $N{=}1$ supersymmetric electrodynamics”, Theoret. and Math. Phys., 147:2 (2006), 687–697
3. K. V. Stepanyantz, “Summation of diagrams in $N=1$ supersymmetric electrodynamics regularized by higher derivatives”, Theoret. and Math. Phys., 146:3 (2006), 321–334
4. 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
5. 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
6. A. B. Pimenov, K. V. Stepanyantz, “Verifying a new identity for Green's functions of the $N=1$ supersymmetric non-Abelian Yang–Mills theory with matter fields”, Theoret. and Math. Phys., 156:2 (2008), 1199–1208
7. Soloshenko AA, Stepan'yants KV, “Schwinger-Dyson Equations for N=1 Supersymmetric Yang-Mills Theory”, Moscow University Physics Bulletin, 63:3 (2008), 189–192
8. Pimenov, AB, “REGULARIZATION BY HIGHER DERIVATIVES AND QUANTUM CORRECTION FOR N=1 SUPERSYMMETRIC THEORIES”, Russian Physics Journal, 51:5 (2008), 444
9. Stepanyantz, KV, “Toward proving a new identity for Green's functions in N=1 supersymmetric electrodynamics”, Physics of Atomic Nuclei, 72:1 (2009), 105
10. Shevtsova, ES, “Structure of the two-point green function of the gauge field for N=1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives”, Moscow University Physics Bulletin, 64:5 (2009), 485
11. Stepanyantz, KV, “A new relation restricting the Green functions of N=1 supersymmetric electrodynamics”, Moscow University Physics Bulletin, 64:3 (2009), 250
12. Stepanyantz K., “Application of Higher Derivative Regularization To Calculation of Quantum Corrections in N=1 Supersymmetric Theories”, Particle Physics on the Eve of Lhc, 2009, 390–393
13. Pimenov A.B., Shevtsova E.S., Stepanyantz K.V., “Calculation of two-loop beta-function for general N=1 supersymmetric Yang-Mills theory with the higher covariant derivative regularization”, Physics Letters B, 686:4–5 (2010), 293–297
14. K. V. Stepanyantz, “Higher covariant derivative regularization for calculations in supersymmetric theories”, Proc. Steklov Inst. Math., 272 (2011), 256–265
15. Stepanyantz K.V., “Derivation of the exact NSVZ beta-function in N=1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams”, Nuclear Phys B, 852:1 (2011), 71–107
16. Stepanyantz K.V., “Factorization of Integrals Defining the beta-Function into Integrals of Total Derivatives in N=1 SQED, Regularized by Higher Derivatives”, Internat J Theoret Phys, 51:1 (2012), 276–291
17. Stepanyantz K.V., “Multiloop Calculations in Supersymmetric Theories with the Higher Covariant Derivative Regularization”, 14th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (Acat 2011), Journal of Physics Conference Series, 368, ed. Teodorescu L., IOP Publishing Ltd, 2012, 012052
18. Stepanyantz K.V., “Derivation of the Exact Nsvz Beta-Function in N=1 Sqed Regularized by Higher Derivatives by Summation of Feynman Diagrams”, 7th International Conference on Quantum Theory and Symmetries (Qts7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012115
19. Kataev A.L. Stepanyantz K.V., “NSVZ Scheme with the Higher Derivative Regularization for N=1 Sqed”, Nucl. Phys. B, 875:2 (2013), 459–482
20. A. L. Kataev, K. V. Stepanyantz, “The NSVZ $\beta$-function in supersymmetric theories with different regularizations and renormalization prescriptions”, Theoret. and Math. Phys., 181:3 (2014), 1531–1540
21. Stepanyantz K.V., “The Nsvz Beta-Function and the Schwinger-Dyson Equations For N=1 Sqed With N-F Flavors, Regularized By Higher Derivatives”, J. High Energy Phys., 2014, no. 8, 096
22. Buchbinder I.L. Stepanyantz K.V., “The Higher Derivative Regularization and Quantum Corrections in N=2 Supersymmetric Theories”, Nucl. Phys. B, 883 (2014), 20–44
23. Kataev A.L. Stepanyantz K.V., “Scheme Independent Consequence of the Nsvz Relation For N=1 Sqed With N-F Flavors”, Phys. Lett. B, 730 (2014), 184–189
24. Shifman M. Stepanyantz K., “Exact Adler Function in Supersymmetric QCD”, Phys. Rev. Lett., 114:5 (2015), 051601
25. Buchbinder I.L., Pletnev N.G., Stepanyantz K.V., “Manifestly N=2 Supersymmetric Regularization For N=2 Supersymmetric Field Theories”, Phys. Lett. B, 751 (2015), 434–441
26. JETP Letters, 103:2 (2016), 77–81
27. Stepanyantz K.V., Nucl. Phys. B, 909 (2016), 316–335
28. Aleshin S.S. Kazantsev A.E. Skoptsov M.B. Stepanyantz K.V., “One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization”, J. High Energy Phys., 2016, no. 5, 014
29. I. V. Nartsev, K. V. Stepanyantz, “NSVZ-like scheme for the photino mass in softly broken $N=1$ SQED regularized by higher derivatives”, JETP Letters, 105:2 (2017), 69–73
30. Aleshin S.S. Goriachuk I.O. Kataev A.L. Stepanyantz K.V., Phys. Lett. B, 764 (2017), 222–227
31. Shakhmanov V.Yu. Stepanyantz K.V., “Three-Loop Nsvz Relation For Terms Quartic in the Yukawa Couplings With the Higher Covariant Derivative Regularization”, Nucl. Phys. B, 920 (2017), 345–367
32. Nartsev I.V. Stepanyantz K.V., “Exact renormalization of the photino mass in softly broken $\mathcal{N}=1$ SQED with $N_f$ flavors regularized by higher derivatives”, J. High Energy Phys., 2017, no. 4, 047
33. Shakhmanov V.Yu. Stepanyantz K.V., “New Form of the Nsvz Relation At the Two-Loop Level”, Phys. Lett. B, 776 (2018), 417–423
34. Kataev A.L. Kazantsev A.E. Stepanyantz K.V., “The Adler D-Function For N=1 SQCD Regularized By Higher Covariant Derivatives in the Three-Loop Approximation”, Nucl. Phys. B, 926 (2018), 295–320
35. Kazantsev A.E. Shakhmanov V.Yu. Stepanyantz K.V., “New Form of the Exact Nsvz Beta-Function: the Three-Loop Verification For Terms Containing Yukawa Couplings”, J. High Energy Phys., 2018, no. 4, 130
36. Kazantsev A.E. Kuzmichev M.D. Meshcheriakov N.P. Novgorodtsev S.V. Shirokov I.E. Skoptsov M.B. Stepanyantz K.V., “Two-Loop Renormalization of the Faddeev-Popov Ghosts in N=1 Supersymmetric Gauge Theories Regularized By Higher Derivatives”, J. High Energy Phys., 2018, no. 6, 020
37. Aleshin S.S., “Nsvz Relation and the Dimensional Reduction in N=1 Sqed”, Phys. Part. Nuclei, 49:5 (2018), 966–968
38. Stepanyantz K., Xxv International Conference on Integrable Systems and Quantum Symmetries (Isqs-25), Journal of Physics Conference Series, 965, IOP Publishing Ltd, 2018
39. Aleshin S.S. Kataev A.L. Stepanyantz K.V., “The Three-Loop Adler D-Function For N=1 Sqcd Regularized By Dimensional Reduction”, J. High Energy Phys., 2019, no. 3, 196
40. Kataev A.L. Kazantsev A.E. Stepanyantz K.V., “On-Shell Renormalization Scheme For N=1 Sqed and the Nsvz Relation”, Eur. Phys. J. C, 79:6 (2019), 477
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