Is There Scale Invariance in N=1 Supersymmetric Field Theories ?

Details Is There Scale Invariance in N=1 Supersymmetric Field Theories ? Is There Scale Invariance in N=1 Supersymmetric Field Theories ?

2011-03-21

arxiv.org/abs/1103.3948v3

Physics

High Energy Physics

High Energy Physics - Theory

v3: 13 pages, major revision

Scientific paper

In two dimensions, it is well known that the scale invariance can be considered as conformal invariance. However, there is no solid proof of this equivalence in four or higher dimensions. In this paper, following recent discussions on this potential discrepancy in $R$-symmetric $\mathcal{N}=1$ supersymmetric field theories, we consider supersymmetric theories without conserved $R$ symmetry, whose supercurrent multiplets can be described either by $\mathcal{S}$ or FZ multiplet. We discover that there are no possibilities for these theories to be scale invariant. Based on these observations, we conclude that $R$ symmetry is a necessary condition for $\mathcal{N}=1$ scale invariant supersymmetric field theories, although the structure of group for supersymmetric fixed points does not contain the $R$ generator. This fact also implicitly indicates that there is probably no discrepancy between scale and conformal invariance.

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