Abstract
We analyse the relation between anomalies in their manifestly supersymmetric formulation in superspace and their formulation in Wess–Zumino (WZ) gauges. We show that there is a one-to-one correspondence between the solutions of the cohomology problem in the two formulations and that they are related by a particular choice of a superspace counterterm (‘scheme’). Any apparent violation of Q-supersymmetry is due to an explicit violation by the counterterm which defines the scheme equivalent to the WZ gauge. It is therefore removable.
Highlights
We analyse the relation between anomalies in their manifestly supersymmetric formulation in superspace and their formulation in Wess-Zumino (WZ) gauges
We could be more specific about the shifting of the anomalies we used: comparing with the minimal Q-symmetric scheme it is evident that Q-supersymmetry became anomalous when we gauged away the Sm field, even though the required transformation δSm = sm with ∂msm = 0 is anomalous
While anomalies in supersymmetric theories obey the general constraints of any relativistic QFT following from analyticity and unitarity, they have specific features caused mainly by the proliferation of “ultralocal null operators”
Summary
We mostly review well known facts. They are discussed in detail in [8, 9] and more recently in [10]. C ≡ i d4x d2θ Λ0 W αWα + h.c. and the counterterm corrected generating functional has the following properties: a) its anomaly reproduces (2.10) b) it depends only on the V -components in the WZ gauge. There are purely local terms contained in Γ[V ] which are linear in the sources (C, χ, M) They can be read off from the component expansion of the counterterm C and the fact that Γ[V ] is independent of them. The local correlators derived from the counterterm C have to be added by hand They contain components of J whose sources are absent in Γ, but they can be recovered as explained in general terms in the introduction and explicitely for the U(1) flavour current
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