A Candidate for a Supergravity Anomaly

TL;DR

This paper explores a novel supergravity anomaly arising from a specific triangle diagram involving gravitinos and gauge bosons, analyzing its conditions and implications for spontaneous symmetry breaking.

Contribution

It introduces a new type of supergravity anomaly linked to a unique triangle diagram and discusses conditions under which it appears or can be canceled.

Findings

Anomaly appears only with spontaneous supergravity breaking.

Anomaly coefficient is zero in unbroken supersymmetry.

Removing the anomaly requires purely chiral breaking with <F^i> ≠ 0 and <D^a>=0.

Abstract

Using elementary BRS cohomology theory, this paper describes a supergravity anomaly analogous to, but very different from, the well known gauge and gravitational anomalies. It closely resembles the known gauge anomalies, but it results from a triangle diagram with two gravitinos and a gauge vector boson, rather than three gauge vector bosons, or two gravitons and a vector boson. A model that is likely to generate this supergravity anomaly is described. The coefficient of this anomaly, in perturbation theory, in a theory with unbroken supersymmetry, appears to be zero, because no relevant diagrams are linearly divergent. However, when, and only when, the theory has spontaneously broken supergravity, there are counterterms in the action which contribute to linearly divergent diagrams that can generate the anomaly. From the relevant Feynman diagrams in the theory, the general form of the anomaly can be conjectured. It is proportional to the VEV $\left< D^a \right>$ of the auxiliary field for the vector boson. So removing the anomaly generates a requirement that the effective spontaneous breaking of supergravity needs to be of the purely chiral type with $\left< F^i \right> \not = 0$ and with $\left< D^a \right>=0$.