Induced Field Theory on the Brane World - Gravity, Extrinsic Curvature, and Gauge Fields

TL;DR

This paper develops a framework for deriving gravity, extrinsic curvature, and gauge fields on a brane world, demonstrating their induced nature and deriving an explicit solitonic solution in five dimensions.

Contribution

It introduces a method to induce field theories on branes, incorporating geometric constraints and providing explicit solutions for curved domain walls.

Findings

Gravity, extrinsic curvature, and gauge fields are induced on the brane.

The induced fields obey Gauss-Codazzi-Ricci equations alongside their equations of motion.

Explicit solitonic solution for a curved domain wall in five dimensions is derived.

Abstract

We show how the gravity, extrinsic curvature, and gauge field theories are induced on dynamically localized brane world. They should obey the Gauss-Codazzi-Ricci equation in addition to their own equations of motion. As an example, we derive the solitonic solution for curved domain wall in five dimensions in terms of gravity and extrinsic curvature fields of the brane, and then derive the effective action for their field theory on the brane.