Worldline approach to vector and antisymmetric tensor fields II

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).

23 pages, 3 figures

References in corpus (6)

• Worldline formalism in a gravitational background
• Trace Anomalies from Quantum Mechanics
• Worldline approach to vector and antisymmetric tensor fields
• The Path Integral for a Particle in Curved Spaces and Weyl Anomalies
• Dimensional regularization for N=1 susy sigma models and the worldline formalism
• BRST treatment of zero modes for the worldline formalism in curved space

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