Discretizing Gravity in Warped Spacetime

TL;DR

This paper explores a lattice discretization of the Randall-Sundrum warped spacetime model, showing it captures key features of the continuum theory and offers a practical approach for studying gravity in curved space.

Contribution

It demonstrates that lattice discretization of warped spacetime models preserves essential physics and is effective in the holographic regime, despite limitations in taking the continuum limit.

Findings

Strong coupling scale is independent of IR scale and lattice size in warped space.

Lattice theory reproduces key features of warped spacetime and is advantageous over KK theory.

Lattice approach is promising for studying gravity in curved spacetime.

Abstract

We investigate the discretized version of the compact Randall-Sundrum model. By studying the mass eigenstates of the lattice theory, we demonstrate that for warped space, unlike for flat space, the strong coupling scale does not depend on the IR scale and lattice size. However, strong coupling does prevent us from taking the continuum limit of the lattice theory. Nonetheless, the lattice theory works in the manifestly holographic regime and successfully reproduces the most significant features of the warped theory. It is even in some respects better than the KK theory, which must be carefully regulated to obtain the correct physical results. Because it is easier to construct lattice theories than to find exact solutions to GR, we expect lattice gravity to be a useful tool for exploring field theory in curved space.