Curvature as a remedy or discretizing gravity in warped dimensions

TL;DR

This paper explores how introducing curvature in warped extra dimensions can address issues in discretizing gravity, particularly the problematic long-wavelength modes, although challenges reappear at smaller scales.

Contribution

It demonstrates that curvature in warped dimensions can mitigate discretization problems in gravity models, providing a potential solution to flat space issues.

Findings

Curvature alleviates long-wavelength mode problems in discretized gravity.

Problems re-emerge at scales smaller than the bulk curvature.

Warped dimensions offer a promising approach for discretizing gravity.

Abstract

The attempt to discretize gravity in flat space is foiled by the appearance of strongly interacting long wave-length longitudinal modes. In this paper we show how the introduction of sites with different scales, or equivalently curvature in the bulk, ameliorate all the problems encountered in flat space associated with long wave-length modes. However, as one could expect, all such problem resurface once the mode's wave-length is smaller than the bulk curvature.