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.

在本文中，我们将考虑在三个时空维度上无质量引力的无穷多个协变导数的最一般的二次曲率作用。广义相对论中，该动作是奇偶不变且无扭转的，并且包含与爱因斯坦-希尔伯特动作相同的脱壳自由度。在紫外线，用给定的传播的适当选择的整个功能的指数，可以将点状曲率奇点平滑化为高斯分布，而在红外中，该理论简化为广义相对论。我们还将展示如何在Minkowski背景中将新的大质量重力嵌入到无鬼影的无限导数重力中，作为红外极限之一。最后，我们将通过扰动几何形状，在三维空间中存在deSitter和Anti-deSitter时空中的宇宙常数的情况下，提供无限微分引力的树级统一性条件。