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Tr. Mat. Inst. Steklova, 2020, Volume 309, Pages 304–319 (Mi tm4064)  

The Higher Covariant Derivative Regularization as a Tool for Revealing the Structure of Quantum Corrections in Supersymmetric Gauge Theories

K. V. Stepanyantz

Faculty of Physics, Moscow State University, Moscow, 119991 Russia

Abstract: We discuss why the Slavnov higher covariant derivative regularization appeared to be an excellent instrument for investigating quantum corrections in supersymmetric gauge theories. For example, it allows demonstrating that the $\beta $-function in these theories is given by integrals of double total derivatives and to construct the Novikov–Shifman–Vainshtein–Zakharov (NSVZ) renormalization prescription in all loops. It was also used to derive the non-renormalization theorem for the triple gauge-ghost vertices. With the help of this theorem the exact NSVZ $\beta $-function was rewritten in a new form, which revealed its perturbative origin. Moreover, in the case of using the higher covariant derivative regularization, it is possible to construct a method for obtaining the $\beta $-function of $\mathcal N=1$ supersymmetric gauge theories, which simplifies the calculations to a great extent. This method is illustrated by an explicit two-loop calculation made in the general $\xi $-gauge.

Funding Agency Grant Number
Foundation for the Development of Theoretical Physics and Mathematics BASIS 19-1-1-45-1
This work was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS,” project no. 19-1-1-45-1.


DOI: https://doi.org/10.4213/tm4064

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 309, 284–298

Bibliographic databases:

UDC: 530.145
Received: September 26, 2019
Revised: October 30, 2019
Accepted: January 4, 2020

Citation: K. V. Stepanyantz, “The Higher Covariant Derivative Regularization as a Tool for Revealing the Structure of Quantum Corrections in Supersymmetric Gauge Theories”, Modern problems of mathematical and theoretical physics, Collected papers. On the occasion of the 80th birthday of Academician Andrei Alekseevich Slavnov, Tr. Mat. Inst. Steklova, 309, Steklov Math. Inst. RAS, Moscow, 2020, 304–319; Proc. Steklov Inst. Math., 309 (2020), 284–298

Citation in format AMSBIB
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\paper The Higher Covariant Derivative Regularization as a Tool for Revealing the Structure of Quantum Corrections in Supersymmetric Gauge Theories
\inbook Modern problems of mathematical and theoretical physics
\bookinfo Collected papers. On the occasion of the 80th birthday of Academician Andrei Alekseevich Slavnov
\serial Tr. Mat. Inst. Steklova
\yr 2020
\vol 309
\pages 304--319
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
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\vol 309
\pages 284--298
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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