Deformations of Supergravity and Supersymmetry Anomalies

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 $\mathrm{U}(1){}_{\mathrm{R}}$ 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 $\mathrm{U}(1){}_{\mathrm{R}}$ 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 $S_1$ of ghost number 1. We give a cohomological characterization of $S_1$ 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.

28 pages, includes Mathematica notebook. Clarified relation to the BRST cohomology in the antifield formalism, new reference

References in corpus (4)

• Anomalous Supersymmetry
• Quantum consistency in supersymmetric theories with $R$-symmetry in curved space
• Consistency of supersymmetric 't Hooft anomalies
• Anomalies and Supersymmetry

Cited by in corpus (3)

• Superconformal anomalies from superconformal Chern-Simons polynomials
• Anomalies and Supersymmetry
• Kodaira-Spencer Anomalies with Stora-Zumino Method