Abstract:
We briefly review the calculations of quantum corrections related to the exact Novikov–Shifman–Vainshtein–Zakharov (NSVZ) β-function in 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 β-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 β-function leads to a certain scheme-independent equality.
Citation:
A. L. Kataev, K. V. Stepanyantz, “The NSVZ β-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
\Bibitem{KatSte14}
\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
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\jour Theoret. and Math. Phys.
\yr 2014
\vol 181
\issue 3
\pages 1531--1540
\crossref{https://doi.org/10.1007/s11232-014-0233-3}
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Linking options:
https://www.mathnet.ru/eng/tmf8721
https://doi.org/10.4213/tmf8721
https://www.mathnet.ru/eng/tmf/v181/i3/p475
This publication is cited in the following 61 articles:
A. L. Kataev, K. V. Stepanyantz, “Exact Relations Between Running of αs and α in N = 1 SQCD + SQED”, Jetp Lett., 2025
I. E. Shirokov, V. Yu. Shirokova, “The four-loop β-function from vacuum supergraphs and the NSVZ relation for N=1 SQED regularized by higher derivatives”, Eur. Phys. J. C, 84:3 (2024)
K. V. Stepanyantz, “Quantum Corrections and Exact Results in Supersymmetric Theories Regularized by Higher Covariant Derivatives”, Moscow Univ. Phys., 79:S1 (2024), 486
K. V. Stepanyantz, “The structure of quantum corrections and exact results in supersymmetric theories from the higher covariant derivative regularization”, Theoret. and Math. Phys., 217:3 (2023), 1954–1968
S. S. Aleshin, K. V. Stepanyantz, “Quantum properties of gauge theories with extended supersymmetry formulated in
N=1
superspace”, Phys. Rev. D, 107:10 (2023)
I. E. SHIROKOV, “COMPUTER ALGEBRA CALCULATIONS IN SUPERSYMMETTIC
LECTRODYNAMICS”, Programmirovanie, 2023, no. 2, 69
Dmitri Bykov, “β-function of the level-zero Gross–Neveu model”, SciPost Phys., 15:4 (2023), 127–27
I. E. Shirokov, “Computer Algebra Calculations in Supersymmetric Electrodynamics”, Program Comput Soft, 49:2 (2023), 122
N. P. Meshcheriakov, V. V. Shatalova, K. V. Stepanyantz, “Higher logarithms and ε-poles for the MS-like renormalization prescriptions”, J. High Energ. Phys., 2023:12 (2023)
Kuzmichev M., Meshcheriakov N., Novgorodtsev S., Shatalova V., Shirokov I., Stepanyantz K., “Finiteness of the Triple Gauge-Ghost Vertices in N=1 Supersymmetric Gauge Theories: the Two-Loop Verification”, Eur. Phys. J. C, 82:1 (2022), 69
I. E. Shirokov, K. V. Stepanyantz, “The three-loop anomalous dimension and the four-loop β-function for N = 1 SQED regularized by higher derivatives”, J. High Energ. Phys., 2022:4 (2022)
Matteo Becchetti, Marco Bochicchio, “Operator mixing in massless QCD-like theories and Poincarè–Dulac theorem”, Eur. Phys. J. C, 82:10 (2022)
O. V. Haneychuk, V. Yu. Shirokova, K. V. Stepanyantz, “Three-loop β-functions and two-loop anomalous dimensions for MSSM regularized by higher covariant derivatives in an arbitrary supersymmetric subtraction scheme”, J. High Energ. Phys., 2022:9 (2022)
Matteo Becchetti, “A differential-geometry approach to operator mixing in massless QCD-like theories and Poincaré-Dulac theorem”, SciPost Phys. Proc., 2022, no. 7
Konstantin Stepanyantz, “NSVZ \boldsymbol{\beta}-Function and NSVZ Scheme with the Higher Covariant Derivative Regularization in the Non-Abelian Case”, Moscow Univ. Phys., 77:2 (2022), 474
Kuzmichev M.D., Meshcheriakov N.P., Novgorodtsev V S., Shirokov I.E., Stepanyantz V K., “Finiteness of the Two-Loop Matter Contribution to the Triple Gauge-Ghost Vertices in N=1 Supersymmetric Gauge Theories Regularized By Higher Derivatives”, Phys. Rev. D, 104:2 (2021), 025008
Stepanyantz K.V., “Exact Beta-Functions For N=1 Supersymmetric Theories Finite in the Lowest Loops”, Eur. Phys. J. C, 81:7 (2021), 571
Cherchiglia A., Arias-Perdomo D.C., Vieira A.R., Sampaio M., Hiller B., “Two-Loop Renormalisation of Gauge Theories in 4D Implicit Regularisation and Connections to Dimensional Methods”, Eur. Phys. J. C, 81:5 (2021), 468
D. S. Korneev, D. V. Plotnikov, K. V. Stepanyantz, N. A. Tereshina, “The NSVZ relations for \mathcal{N} = 1 supersymmetric theories with multiple gauge couplings”, J. High Energ. Phys., 2021:10 (2021)
K. V. Stepanyantz, “The Higher Covariant Derivative Regularization as a Tool for Revealing the Structure of Quantum Corrections in Supersymmetric Gauge Theories”, Proc. Steklov Inst. Math., 309 (2020), 284–298
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