Anomaly Mediated Gaugino Mass and Path-Integral Measure

In recent years, there has been controversy concerning the anomaly-mediated gaugino mass in the superspace formalism of supergravity. In this paper, we reexamine the gaugino mass term in this formalism by paying particular attention to the symmetry that controls gaugino masses in supergravity. We first discuss super-diffeomorphism invariance of path-integral measures of charged superfields. As we will show, the super-diffeomorphism-invariant measure is not invariant under a super-Weyl transformation, which is the origin of the anomaly-mediated gaugino mass. We show how the anomaly-mediated gaugino mass is expressed as a local operator in a Wilsonian effective action in a super-diffeomorphism-covariant way. We also obtain a gaugino mass term independent of the gauge choice of the fictitious super-Weyl symmetry in the super-Weyl compensator formalism, which reproduces the widely accepted result. We also discuss how to reconcile the gaugino mass term in the local Wilsonian effective action and the gaugino mass term appearing in a nonlocal one-particle irreducible quantum effective action.

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36 pages

12.60.Jv
04.65.+e
gaugino: mass
gaugino: mediation
mediation: anomaly
path integral: measure
operator: local
effective action
supergravity
superspace

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