Regularization of Brane Induced Gravity

TL;DR

This paper investigates the regularization of brane-induced gravity in higher dimensions, demonstrating a four-dimensional gravitation at small scales due to a massive resonance, and ensuring the theory is ghost-free.

Contribution

It introduces a regularization scheme for brane-induced gravity in codimension greater than one, showing the emergence of 4D gravity and stability of the theory.

Findings

Four-dimensional gravity arises at distances below a critical scale.

The resonance mass determines the crossover scale.

The theory is free of ghosts and tachyons.

Abstract

We study the regularization of theories of ``brane induced'' gravity in codimension $N>1$. The brane can be interpreted as a thin dielectric with a large dielectric constant, embedded in a higher dimensional space. The kinetic term for the higher dimensional graviton is enhanced over the brane. A four dimensional gravitation is found on the brane at distances smaller than a critical distance $r<r_c$, and is due to the exchange of a massive resonant graviton. The crossover scale $r_c$ is determined by the mass of the resonance. The suppression of the couplings of light Kaluza-Klein modes to brane matter results in a higher dimensional force law at large distances. We show that the resulting theory is free of ghosts or tachyons.