Dynamical Foundations of the Brane Induced Gravity

TL;DR

This paper develops a formalism to derive the induced gravity on a brane, showing how quantum fluctuations lead to Einstein-like equations and identifying unique features of brane-induced gravity.

Contribution

It provides a comprehensive derivation of the induced gravity equations from brane dynamics, including quantum effects and extrinsic curvature terms, highlighting features distinct from traditional gravity theories.

Findings

Quantum fluctuations induce Einstein-like equations on the brane.

Coefficients of gravity and cosmological terms are explicitly determined.

Normal connection gauge fields are characteristic of brane-induced gravity.

Abstract

We present a comprehensive formalism to derive precise expressions for the induced gravity of the braneworld, assuming the dynamics of the Dirac-Nambu-Goto type. The quantum fluctuations of the brane at short distances give rise to divergences, which should be cutoff at the scale of the inverse thickness of the brane. It turns out that the induced-metric formula is converted into an Einstein-like equation via the quantum effects. We determine the coefficients of the induced cosmological and gravity terms, as well as those of the terms including the extrinsic curvature and the normal connection gauge field. The latter is the characteristic of the brane induced gravity theory, distinguished from ordinary none-brane induced gravity.