Self-dual formulations of D = 3 gravity theories

Abstract

We present a novel description of linearized topologically massive gravity in which the connections, rather than metrics or dreibeins, are the fundamental variables, thereby reducing the derivative order from third ro second. The “metricity” of the affinities is implied by the field equations. The ostensible “Einstein” and “Chern-Simons” terms in the action each generate the other tensor in the field equations. The “Chern-Simons” term by itself actually represents a first order form of linearized Einstein gravity; we discuss the relation between their nonlinear extensions. We also point out that the self-dual description immediately explains why the vector Chern-Simons term does not induce anyon behavior in its sources when the Higgs term in present.