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. 1982Academic Press

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Expansion of supersymmetric string theory suggests that the leading quadratic curvature correction to the Einstein action is the Gauss-Bonnet invariant. We show that this model has both flat and anti -de Sitter space as solutions, but that the cosmological branch is unstable, because the graviton becomes a ghost there: The theory solves its own cosmological problem. The general static spherically symmetric solution is exhibited; it is asymptotically Schwarzschild. The sign of the Gauss-Bonnet coefficient determines whether there is a normal event horizon (for the stringgenerated sign) or a naked singularity. We discuss the effects of higher-curvature corrections and of an explicit cosmological term on stability. We shall conclude that the Gauss-Bonnet combination, unlike any other quadratic terms, leads to a viable theory and that even the sign of its coefficient must be that dictated by the string expansion. This result is all the more remarkable because we shall see that there is an intrinsic cosmological-constant problem in all higher-curvature theories, which this particular model solves in an elegant way.In addition to the asymptotically flat solutions, there is a cosmological, asymptotically anti-de Sitter branch.Such branches are a generic feature of actions with two or more curvature terms not involving explicit derivatives plus any number with derivatives. However, these solutions turn out to be intrinsically unstable: The graviton excitations about this background are ghosts, as is also confirmed by positive-energy sources leading to negative-mass Schwarzschild-anti -de Sitter solutions. We shall also discuss this branch in the presence of higher-order curvature corrections and of an explicit cosmological term, with qualitatively similar conclusions.The action we consider has the form