Quantum Inconsistency of Einstein Supergravity

TL;DR

This paper demonstrates that N=1, D=4 Einstein supergravity is inconsistent at one loop due to a local supersymmetry anomaly, which can be canceled by adding a Jacobian from super-Weyl transformations, ensuring frame independence.

Contribution

It identifies a one-loop anomaly in Einstein supergravity and proposes a Jacobian correction from super-Weyl transformations to restore consistency.

Findings

Anomaly in local supersymmetry at one loop in Einstein supergravity.

Jacobian from super-Weyl transformation cancels the anomaly.

Frame independence of scattering amplitudes is maintained with the Jacobian.

Abstract

We show that N=1, D=4 Einstein-frame supergravity is inconsistent at one loop because of an anomaly in local supersymmetry transformations. A Jacobian must be added to the Einstein-frame Lagrangian to cancel this anomaly. We show how the Jacobian arises from the super-Weyl field redefinition that takes the superspace Lagrangian to the Einstein frame. We present an explicit example which demonstrates that the Jacobian is necessary for one-loop scattering amplitudes to be frame independent.