Kähler invariance of N = 1 quantum supergravity

Abstract

The Kähler invariance of the N = 1 supergravity theory is investigated beyond the classical level. In the popular gauge fixing condition e mμ − e μm =0, γ μ ψ μ =0, ∂ μ (√ g g μν ) = 0 one has a manifestly Kähler invariant theory at the quantum level and for that the form of the path integral measure is important. We show that Fujikawa's measure is consistent with quantum Kähler invariance. The integration of the auxiliary fields of the closed algebra theory brings down local determinants ( det G zz ∗ ) − necessary for maintaining the Kähler symmetry at the quantum level. Owing to the gauge independence of the path integral measure Kähler invariance is a gauge independent property.