Quantum inconsistency of Einstein supergravity

We show that N = 1, D = 4 Einstein-frame supergravity is inconsistent at on e loop because of an anomaly in local supersymmetry transformations, A Jaco bian must be added to the Einstein-frame Lagrangian to cancel this anomaly. We show how the Jacobian arises from the super-Weyl field redefinition tha t takes the superspace Lagrangian to the Einstein frame. We present an expl icit example which demonstrates that the Jacobian is necessary for one-loop scattering amplitudes to be frame independent. (C) 2001 Elsevier Science B .V. All rights reserved.