Brane Induced Gravity in the Curved Bulk

TL;DR

This paper derives the quantum induced effects on a brane embedded in a curved bulk, accounting for bulk curvature, extrinsic curvature, and normal connection gauge fields, using an invariant formalism based on Riemannian coordinates.

Contribution

It provides a systematic derivation of quantum effects on branes in curved bulks, incorporating geometric quantities like extrinsic curvature and normal connection fields.

Findings

Explicit expressions for quantum induced effects are obtained.

Bulk curvature influences brane fluctuations and induced effects.

The formalism allows invariant definition of brane fluctuations.

Abstract

Starting with the Nambu-Goto action of the braneworld embedded in a curved bulk, we derive the precise expressions for the quantum induced effects due to small fluctuations of the brane. To define the brane fluctuations invariantly, we introduce the Riemannian coordinate system for the subspace normal to the braneworld. It will turn out that we can systematically incorporate the effects of bulk curvature, and that the induced effects depend on the extrinsic curvature and the normal-connection gauge field as well as on bulk curvature components at the brane.