Abstract
We solve the Wess-Zumino consistency conditions of mathcal{N}=1 off-shell conformal supergravity in four dimensions and determine the general form of the superconformal anomalies for arbitrary a and c anomaly coefficients to leading non trivial order in the gravitino. Besides the well known Weyl and R-symmetry anomalies, we compute explicitly the fermionic mathcal{Q} - and mathcal{S} -supersymmetry anomalies. In particular, we show that mathcal{Q} -supersymmetry is anomalous if and only if R-symmetry is anomalous. The mathcal{Q} - and mathcal{S} -supersymmetry anomalies give rise to an anomalous supersymmetry transformation for the supercurrent on curved backgrounds admitting Killing spinors, resulting in a deformed rigid supersymmetry algebra. Our results may have implications for supersymmetric localization and supersymmetry phenomenology. Analogous results are expected to hold in dimensions two and six and for other supergravity theories. The present analysis of the Wess-Zumino consistency conditions reproduces the holographic result of arXiv:1703.0429 and generalizes it to arbitrary a and c anomaly coefficients.
Highlights
In flat space, global — or rigid — anomalies are typically visible only in higher-point functions as contact terms that violate the classical Ward identities
Global anomalies become manifest at the level of the quantum effective action and in one-point functions when arbitrary sources for the current operators are turned on, or when the theory is put on a curved background admitting Killing symmetries
Based on the classical supersymmetry algebra on curved backgrounds that admit a certain number of supercharges, the authors of [30,31,32] demonstrated that the supersymmetric partition function on such backgrounds should be independent of specific deformations of the supersymmetric background
Summary
We turn to the derivation of the classical Ward identities of a local quantum field theory coupled to background N = 1 conformal supergravity. These identities can be thought of as Noether’s conservation laws following from the local symmetry transformations (2.5). Given the definition of the current operators (3.2) and the local symmetry transformations of the background supergravity fields (2.5), classical invariance of W [e, A, ψ] leads to a conservation law — or Ward identity — for each local symmetry, which we will derive. The transformation of the generating functional under diffeomorphisms is given by δξW = d4x e δξeaμTaμ + δξAμJ μ + δξψμSμ Setting this quantity to zero for arbitrary ξν(x) gives the classical diffeomorphism Ward identity eaμ∇ν Taν. And the classical Ward identity for S-supersymmetry is γμ S μ (3.15) (3.16)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
