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TMF, 2014, Volume 181, Number 3, Pages 475–486 (Mi tmf8721)  

This article is cited in 25 scientific papers (total in 25 papers)

The NSVZ $\beta$-function in supersymmetric theories with different regularizations and renormalization prescriptions

A. L. Kataeva, K. V. Stepanyantzb

a Institute for Nuclear Research, RAS, Moscow, Russia
b Lomonosov Moscow State University, Moscow, Russia

Abstract: We briefly review the calculations of quantum corrections related to the exact Novikov–Shifman–Vainshtein–Zakharov (NSVZ) $\beta$-function in $\mathcal{N}=1$ supersymmetric theories, paying special attention to the scheme dependence of the results. We explain how the NSVZ relation is obtained for the renormalization group functions defined in terms of the bare coupling constant if a theory is regularized by higher derivatives. We also describe how to construct a special renormalization prescription that gives the NSVZ relation for the renormalization group functions defined in terms of the renormalized coupling constant exactly in all orders for Abelian supersymmetric theories regularized by higher derivatives and discuss the scheme dependence of the NSVZ $\beta$-function (for the renormalization group functions defined in terms of the renormalized coupling constant) in the non-Abelian case. We show that in this case, the NSVZ $\beta$-function leads to a certain scheme-independent equality.

Keywords: supersymmetry, renormalization, $\beta$-function


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English version:
Theoretical and Mathematical Physics, 2014, 181:3, 1531–1540

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Document Type: Article
Received: 31.05.2014

Citation: A. L. Kataev, K. V. Stepanyantz, “The NSVZ $\beta$-function in supersymmetric theories with different regularizations and renormalization prescriptions”, TMF, 181:3 (2014), 475–486; Theoret. and Math. Phys., 181:3 (2014), 1531–1540

Citation in format AMSBIB
\by A.~L.~Kataev, K.~V.~Stepanyantz
\paper The~NSVZ $\beta$-function in supersymmetric theories with different
regularizations and renormalization prescriptions
\jour TMF
\yr 2014
\vol 181
\issue 3
\pages 475--486
\jour Theoret. and Math. Phys.
\yr 2014
\vol 181
\issue 3
\pages 1531--1540

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    This publication is cited in the following articles:
    1. M. Shifman, K. Stepanyantz, “Exact Adler function in supersymmetric QCD”, Phys. Rev. Lett., 114:5 (2015), 051601  crossref  adsnasa  isi  scopus
    2. I. L. Buchbinder, N. G. Pletnev, K. V. Stepanyantz, “Manifestly $\mathcal N=2$ supersymmetric regularization for $\mathcal N=2$ supersymmetric field theories”, Phys. Lett. B, 751 (2015), 434–441  crossref  adsnasa  isi  elib  scopus
    3. JETP Letters, 103:2 (2016), 77–81  mathnet  crossref  crossref  isi  elib
    4. A. L. Cherchiglia, M. Sampaio, B. Hiller, A. P. Baeta Scarpelli, “Subtleties in the beta-function calculation of $\mathcal N=1$ supersymmetric gauge theories”, Eur. Phys. J. C, 76:2 (2016), 47  crossref  mathscinet  adsnasa  isi  scopus
    5. G. Choi, R. Shrock, “Integral formalism for the construction of scheme transformations in quantum field theory”, Phys. Rev. D, 94:6 (2016), 065038  crossref  mathscinet  isi  elib  scopus
    6. K. V. Stepanyantz, “Non-renormalization of the $V\overline{c}c$-vertices in $\mathcal{N}=1$ supersymmetric theories”, Nucl. Phys. B, 909 (2016), 316–335  crossref  mathscinet  zmath  isi  elib  scopus
    7. S. S. Aleshin, A. E. Kazantsev, M. B. Skoptsov, K. V. Stepanyantz, “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  crossref  isi  elib  scopus
    8. G. Choi, R. Shrock, “Study of the renormalization-group evolution of $\mathcal{N}=1$ supersymmetric gauge theories using Padé approximants”, Phys. Rev. D, 93:6 (2016), 065013  crossref  mathscinet  isi  elib  scopus
    9. 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  mathnet  crossref  crossref  isi  elib
    10. N. Ambrosetti, D. Arnold, J.-P. Derendinger, J. Hartong, “Gauge coupling field, currents, anomalies and $\mathcal N=1$ super-Yang–Mills effective actions”, Nucl. Phys. B, 915 (2017), 285–334  crossref  mathscinet  zmath  isi  scopus
    11. S. S. Aleshin, I. O. Goriachuk, A. L. Kataev, K. V. Stepanyantz, “The NSVZ scheme for $\mathcal N =1$ SQED with $N_f$ flavors, regularized by the dimensional reduction, in the three-loop approximation”, Phys. Lett. B, 764 (2017), 222–227  crossref  mathscinet  zmath  isi  scopus
    12. T. A. Ryttov, R. Shrock, “Scheme-independent calculations of physical quantities in an $\mathcal{N}=1$ supersymmetric gauge theory”, Phys. Rev. D, 96:10 (2017), 105018  crossref  isi  scopus
    13. T. A. Ryttov, R. Shrock, “Infrared fixed point physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ gauge theories”, Phys. Rev. D, 96:10 (2017), 105015  crossref  isi  scopus
    14. V. Yu. Shakhmanov, K. V. Stepanyantz, “Three-loop NSVZ relation for terms quartic in the Yukawa couplings with the higher covariant derivative regularization”, Nucl. Phys. B, 920 (2017), 345–367  crossref  mathscinet  zmath  isi  scopus
    15. T. A. Ryttov, R. Shrock, “Higher-order scheme-independent series expansions of $\gamma_{\psi \bar{\psi}\mathrm{, IR}}$ and $\beta'_{\mathrm{IR}}$ in conformal field theories”, Phys. Rev. D, 95:10 (2017)  crossref  isi  scopus
    16. I. V. Nartsev, K. V. Stepanyantz, “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  crossref  mathscinet  isi  scopus
    17. V. Yu. Shakhmanov, K. V. Stepanyantz, “New form of the NSVZ relation at the two-loop level”, Phys. Lett. B, 776 (2018), 417–423  crossref  mathscinet  zmath  isi  scopus
    18. A. L. Kataev, A. E. Kazantsev, K. V. Stepanyantz, “The Adler $D$-function for $\mathcal N=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation”, Nucl. Phys. B, 926 (2018), 295–320  crossref  mathscinet  zmath  isi  scopus
    19. T. A. Ryttov, R. Shrock, “Duality in a supersymmetric gauge theory from a perturbative viewpoint”, Phys. Rev. D, 97:6 (2018), 065020  crossref  isi  scopus
    20. A. E. Kazantsev, V. Yu. Shakhmanov, K. V. Stepanyantz, “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  crossref  mathscinet  zmath  isi
    21. J. A. Gracey, T. A. Ryttov, R. Shrock, “Scheme-independent calculations of anomalous dimensions of baryon operators in conformal field theories”, Phys. Rev. D, 97:11 (2018), 116018  crossref  isi  scopus
    22. A. E. Kazantsev, M. D. Kuzmichev, N. P. Meshcheriakov, S. V. Novgorodtsev, I. E. Shirokov, M. B. Skoptsov, K. V. Stepanyantz, “Two-loop renormalization of the Faddeev-Popov ghosts in $\mathcal N=1$ supersymmetric gauge theories regularized by higher derivatives”, J. High Energy Phys., 2018, no. 6, 020  crossref  mathscinet  isi  scopus
    23. Stepanyantz K.V., “Nsvz Relation in Supersymmetric Theories Regularized By Higher Derivatives”, Phys. Part. Nuclei, 49:5 (2018), 908–910  crossref  mathscinet  isi  scopus
    24. Stepanyantz K., Xxv International Conference on Integrable Systems and Quantum Symmetries (Isqs-25), Journal of Physics Conference Series, 965, IOP Publishing Ltd, 2018  crossref  isi  scopus
    25. Goriachuk I.O., Kataev A.L., Stepanyantz V K., “A Class of the Nsvz Renormalization Schemes For N=1 Sqed”, Phys. Lett. B, 785 (2018), 561–566  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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