Regularization of Brane Induced Gravity

TL;DR

The paper proposes a dielectric-brane regularization for brane-induced gravity in codimension $N>1$, introducing a brane of width $\Delta$ and large contrast to regulate Green functions. It demonstrates that gravity on the brane at short distances is mediated by a massive resonant graviton, producing a 4D Newtonian potential, with a crossover scale $r_c$ set by the resonance mass; at larger distances the force law becomes higher-dimensional due to suppressed couplings of light KK modes. The analysis covers both sharp-boundary and smooth branes, establishing a shape-independent resonance structure and confirming a Pauli-Fierz form for the 4D graviton without ghosts or tachyons. The work also discusses the role of scalar-brane couplings and potential vDVZ-like effects, arguing that the regularization provides a consistent, physically motivated framework for brane-induced gravity in higher codimension with possible implications for cosmology and extra-dimensional phenomenology.

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.