Worldline approach to vector and antisymmetric tensor fields II

TL;DR

This paper extends the worldline approach to include massive vector and antisymmetric tensor fields, deriving a path integral representation for their effective actions, and applies it to compute one-loop graviton self-energy contributions.

Contribution

It introduces a worldline path integral formulation for massive p-form fields and demonstrates how to derive Seeley-DeWitt coefficients and duality relations.

Findings

Derived a proper time expansion for massive p-forms

Showed coefficients shift from massless case by D -> D+1

Calculated one-loop graviton self-energy for massive fields

Abstract

We extend the worldline description of vector and antisymmetric tensor fields coupled to gravity to the massive case. In particular, we derive a worldline path integral representation for the one-loop effective action of a massive antisymmetric tensor field of rank p (a massive p-form) whose dynamics is dictated by a standard Proca-like lagrangian coupled to a background metric. This effective action can be computed in a proper time expansion to obtain the corresponding Seeley-DeWitt coefficients a0, a1, a2. The worldline approach immediately shows that these coefficients are derived from the massless ones by the simple shift D -> D+1, where D is the spacetime dimension. Also, the worldline representation makes it simple to derive exact duality relations. Finally, we use such a representation to calculate the one-loop contribution to the graviton self-energy due to both massless and massive antisymmetric tensor fields of arbitrary rank, generalizing results already known for the massless spin 1 field (the photon).