Abstract
We present a BRST analysis of supersymmetry anomalies of \( \mathcal{N} \) = 1 supersymmetric quantum field theories with anomalous R symmetry. To this end, we consider the coupling of the matter theory to classical \( \mathcal{N} \) = 1 new minimal supergravity. We point out that a supersymmetry anomaly cocycle associated to the U(1)R field does exist for this theory. It is non-trivial in the space of supergravity fields (and ghosts), but it becomes BRST-exact in the functional space that includes antifields. Equivalently, the U(1)R supersymmetry anomaly cocycle vanishes “on-shell”. It is therefore removable. However, to remove it — precisely because it is not trivial in the smaller space of fields — one needs to deform the supergravity BRST operator. This deformation is triggered, at first order in the anomaly coefficient, by a local operator S1 of ghost number 1. We give a cohomological characterization of S1 and compute it in full detail. At higher orders in the anomaly coefficient, we expect a priori that further deformations of the BRST rules are necessary.
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Fröb, M.B., Imbimbo, C. & Risso, N. Deformations of supergravity and supersymmetry anomalies. J. High Energ. Phys. 2021, 9 (2021). https://doi.org/10.1007/JHEP12(2021)009
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DOI: https://doi.org/10.1007/JHEP12(2021)009