Lattice gauge gravity

We propose a lattice gravity action based on the gauge-theory point of view. We avoid a problem, the action potentially going to infinity by taking the link length to a constant $a$ (the lattice constant). By fixing the local Lorentz gauge freedom, we obtain a gauge-fixed version of the $d$-dimensional action as a sum of $a^{d-2\mathrm{}}sin\delta$ ($\delta =\mathrm{deficit}\mathrm{angle}$) which is a compactified version of Regge calculus. The fermion gravity coupling term can be constructed in a similar way. We point out the possibility that this lattice gravity action approaches the Einstein action in the long-range limit if the action has an ultraviolet fixed point.