Renormalization of supersymmetric gauge theory in the uneliminated component formalism

Abstract

We show that the renormalisation of the N = 1 supersymmetric gauge theory when working in the component formalism, without eliminating auxiliary fields and using a standard covariant gauge, requires a non-linear renormalisation of the auxiliary fields.

One-loop renormalization ofN=12supersymmetric gauge theory with a superpotential

“…Although they found divergent contributions which broke supergauge invariance, their final result was gauge-invariant without the need for any redefinition. In subsequent work [14] it was shown that the N = 1 2 superfield action requires modification to ensure renormalisability, which is consistent with our findings in the component formulation [12].…”

“…As we noted in Refs. [11], [12], at the quantum level the U (N ) gauge invariance cannot be retained.…”

“…[8] omitted a few relevant terms). In previous work we have shown that although divergent gauge non-invariant terms are generated at the one-loop level, they can be removed by divergent field redefinitions leading to a renormalisable theory in which N = 1 2 supersymmetry is preserved at the one-loop level in both the pure gauge case [11] and in the presence of chiral matter in the fundamental representation [12]. In the latter case, the joint requirements of renormalisability and N = 1 2 supersymmetry impose the choice of gauge group SU (N ) ⊗U (1) (rather than U (N ) or SU (N )).…”

“…Our purpose here is to repeat the analysis of Ref. [12] for the adjoint case, then proceed to consider the addition of superpotential terms for both the adjoint and fundamental cases, which will turn out to be a non-trivial task. Our goal is to construct a renormalisable N = 1 2 1 See Refs.…”

On the alternative formulation of the three-dimensional noncommutative superspace

“…Afterwards, the perturbative methodology was successfully applied for different N = 2 Wess-Zumino model whose renormalization properties have been discussed in [7][8][9], N = 1 2 supersymmetric gauge theories whose formulation and renormalizability have been studied in [10,11] (see also [12][13][14][15] for discussions on this issue), and extended supersymmetric theories, in particular, those ones formulated in terms of the harmonic superspace [16,17]. The calculation of the superfield effective potential for this kind of theories [18][19][20][21] also deserves to be mentioned.…”