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.
Highlights
Einstein’s theory of general relativity (GR) contains classical and quantum singularities in 3 + 1 spacetime dimensions [1,2]
This paper provides the ghost free conditions for parity invariant and torsion free AIDG in 3d
We found exact maximally symmetric solutions which can serve as background solutions for linearization
Summary
Einstein’s theory of general relativity (GR) contains classical and quantum singularities in 3 + 1 spacetime dimensions [1,2]. It was shown that the full action of ghost-free analytical infinite derivative theory of gravity (AIDG) in 4d can ameliorate the static Schwarzschild blackhole singularity [5,14,15,16,17,18], [19,20] and produces rotating non-singular metrics [21] at linear level. There is an interesting connection between 3d-gravity in AdS and conformal field theory (CFT) in the boundary [41,42] and in AdS3 there exists an intriguing non-trivial blackhole solution [43,44] All these non-trivial features in 3d demand further study on the construction of both massless and massive ghost-free AIDG up to quadratic in curvature.
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