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

K. V. Stepanyantz

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematical and theoretical physics, Tome 309 (2020), pp. 304-319

Résumé

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.