New massless and massive infinite derivative gravity in three dimensions

Abstract: In this paper we will consider the most general quadratic curvature action with infinitely many covariant derivatives of massless gravity in three spacetime dimensions. The action is parity invariant and torsion-free and contains the same off-shell degrees of freedom as the Einstein-Hilbert action in general relativity. In the ultraviolet, with an appropriate choice of the propagator given by the exponential of an entire function, the point-like curvature singularity can be smoothened to a Gaussian distribution, while in the infrared the theory reduces to general relativity. We will also show how to embed new massive gravity in ghost-free infinite derivative gravity in Minkowski background as one of the infrared limits. Finally, we will provide the tree-level unitarity conditions for infinite derivative gravity in presence of a cosmological constant in deSitter and Anti-deSitter spacetimes in three dimensions by perturbing the geometries.