Supersymmetry, quantum corrections, and the higher derivative regularization

Konstantin Stepanyantz,V.E Volkova,D.G Levkov,Y.V Zhezher,V.A Rubakov,V.A Matveev

doi:10.1051/epjconf/201819106002

Abstract

We investigate the structure of quantum corrections in N = 1 supersymmetric theories using the higher covariant derivative method for regularization. In particular, we discuss the non-renormalization theorem for the triple gauge-ghost vertices and its connection with the exact NSVZ β-function. Namely, using the finiteness of the triple gauge-ghost vertices we rewrite the NSVZ equation in a form of a relation between the β-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev-Popov ghosts, and of the matter superfields. We argue that it is this form that follows from the perturbative calculations, and give a simple prescription how to construct the NSVZ scheme in the non-Abelian case. These statements are confirmed by an explicit calculation of the three-loop contributions to the β-function containing Yukawa couplings. Moreover, we calculate the two-loop anomalous dimension of the ghost superfields and demonstrate that for doing this calculation it is very important that the quantum gauge superfield is renormalized non-linearly.

Highlights

IntroductionIn the Abelian case the NSVZ relation is obtained in all orders with the higher derivative regularization for the renormalization group functions (RGFs) defined in terms of the bare coupling constant independently of the renormalization prescription [21, 22]
Investigating of N = 1 supersymmetric gauge theories is very interesting for both phenomenology and theory
In the non-Abelian case the perturbative calculations in the lowest orders produce the new form of the NSVZ equation which relates the β-function to the anomalous dimensions of the quantum gauge superfield, of the Faddeev–Popov ghosts, and of the chiral matter superfields

Summary

Introduction

In the Abelian case the NSVZ relation is obtained in all orders with the higher derivative regularization for the renormalization group functions (RGFs) defined in terms of the bare coupling constant independently of the renormalization prescription [21, 22]. Where the differentiation is made at fixed values of bare parameters, are scheme and regularization dependent and satisfy the NSVZ relation only for a special renormalization prescription To construct this (NSVZ) scheme, we note that, to the N = 1 SQED case considered in [23, 24], for the non-Abelian theories both definitions of RGFs give the same functions, if the boundary conditions. If RGFs defined in terms of the bare couplings satisfy Eq (12) with the higher covariant derivative regularization, HD+MSL=NSVZ

Three-loop verification for terms containing the Yukawa couplings

Two-loop anomalous dimension of the Faddeev–Popov ghosts

Conclusion