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Published April 10, 2000 | public
Journal Article

Topologically Massive Gauge Theories

Abstract

Gauge vector and gravity models are studied in three-dimensional space-time, where novel, gauge invariant, P and T odd terms of topological origin give rise to masses for the gauge fields. In the vector case, the massless Maxwell excitation, which is spinless, becomes massive with spin 1. When interacting with fermions, the quantum theory is infrared and ultraviolet finite in perturbation theory. For non-Abelian models, topological considerations lead to a quantization condition on the dimensionless coupling constant–mass ratio. Ordinary Einstein gravity is trivial, but when augmented by our mass term, it acquires a propagating, massive, spin 2 mode. This theory is ghost-free and causal, although of third-derivative order. Quantum calculations are presented in both the Abelian and non-Abelian vector models, to exhibit some of the delicate aspects of infrared behavior, and regularization dependence.

Additional Information

© 1982 Academic Press. Received 8 July 2008, Accepted 10 July 2008, Available online 17 July 2008. Editor: M. Cvetič. We benefitted from conversations with M. Duff, M. Flato, C. Fronsdal, S. Helgason, C. Isham, J. Schonfeld, D. Sternheimer, G. 't Hooft, and especially E. Witten, who pointed out an error in an earlier version of this paper. These we happily acknowledge.

Additional details

Created:
August 19, 2023
Modified:
October 24, 2023