Quantum Equivalence of Massive Antisymmetric Tensor Field Models in Curved Space

TL;DR

This paper demonstrates that in curved space-time, the effective actions of massive antisymmetric tensor fields are exactly equivalent to those of their classically equivalent vector and scalar fields, using zeta-function identities.

Contribution

It proves the quantum equivalence of massive antisymmetric tensor fields and their vector or scalar counterparts in curved space via zeta-function identities.

Findings

Effective actions for rank-2 tensors equal those for vectors.

Effective actions for rank-3 tensors equal those for scalars.

The proof relies on identities for mass-dependent zeta-functions.

Abstract

We study the effective actions for massive rank-2 and rank-3 antisymmetric tensor field models in curved space-time. These models are classically equivalent to massive vector field and massive scalar field with minimal coupling to gravity respectively. We prove that effective action for massive rank-2 antisymmetric tensor field is exactly equal to one for massive vector field and effective action for massive rank-3 antisymmetric tensor field is exactly equal to one for massive scalar field. Prove is based on an identity for mass-dependent zeta-functions associated with Laplacians acting on $p$-forms.