Renormalization aspects of $$\mathcal {N}=1$$ N = 1 Super Yang–Mills theory in the Wess–Zumino gauge

M A L Capri,S P Sorella,D Vercauteren,M S Guimaraes,L Mihaila,D R Granado,I F Justo

doi:10.1140/epjc/s10052-014-2844-0

Abstract

The renormalization of $$\mathcal {N}=1$$ Super Yang–Mills theory is analyzed in the Wess–Zumino gauge, employing the Landau condition. An all-orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field, and gluino renormalization. The non-renormalization theorem of the gluon–ghost–antighost vertex in the Landau gauge is shown to remain valid in $$\mathcal {N}=1$$ Super Yang–Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess–Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino. These features are explicitly checked through a three-loop calculation.

Highlights

Supersymmetric N = 1 gauge theories exhibit remarkable features, both at perturbative and non-perturbative level; see, for instance, [1] and references therein.For what concerns the ultraviolet behavior, the symmetry between bosons and fermions gives rise to milder divergences in the ultraviolet regime, a property which is at the origin of a set of non-renormalization theorems; see [2].Work supported by FAPERJ, Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro, under the program Cientista do Nosso Estado, E-26/101.578/2010.In this work we discuss some features of the renormalization of N = 1 Super Yang–Mills theories in Euclidean space-time in the Wess–Zumino gauge, in which the number of field components is minimum
4 Three-loop calculation of the renormalization factors ZA and Zλ and check of the non-renormalization theorem of the gluon–ghost–antighost vertex
In this work the issue of the renormalization of N = 1 Super Yang–Mills theory has been addressed in the Wess–Zumino gauge, by employing the Landau condition

Summary

Introduction

In this work we discuss some features of the renormalization of N = 1 Super Yang–Mills theories in Euclidean space-time in the Wess–Zumino gauge, in which the number of field components is minimum. The renormalization factors of all other fields, i.e. the Lagrange multiplier implementing the Landau gauge condition, the Faddeev–Popov ghosts, the external BRST sources, the global SUSY ghosts, etc., can be expressed as suitable combinations of (Zg, Z A, Zλ). As shown in [5,6,7,8,9,10], the most powerful and efficient way to deal with the algebra (1) is constructing a generalized BRST operator Q which collects both gauge and SUSY field transformations, namely. Which enables us to quantize the theory by following the BRST gauge-fixing procedure in a manifestly supersymmetric invariant way.

Da Da 2

Ward identities and algebraic characterization of the invariant counterterm

Ward identities

Conclusion