One-loop renormalisation of N=1/2 supersymmetric gauge theory

Abstract

We show that N = 1 2 supersymmetric gauge theory is renormalisable at one loop, but only after gauge invariance is restored in a non-trivial fashion.

One-loop renormalization of generalN=12supersymmetric gauge theory

“…As we showed in Ref. [8], there are problems with this assumption; even at one loop, at least in the standard class of gauges, divergent non-gauge-invariant terms are generated. However, in the case of pure N = 1 2 supersymmetry (i.e.…”

“…In Ref. [8] we considered the component form of the pure N = 1 2 supersymmetric action adapted to SU (N ). We argued that it was only for SU (N ) that a form-invariant lagrangian could be defined; indeed the U (N ) gauge symmetry is not preserved under renormalisation.…”

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

“…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 )).…”

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.…”