Bridging Dimensions: General Embedding Algorithm and Field-Theory Reconstruction in 5D Braneworld Models

TL;DR

This paper introduces a universal algorithm for embedding 4D geometries into 5D braneworld models and reconstructs supporting field theories, exemplified by a 5D Schwarzschild black hole and de Sitter brane.

Contribution

It presents a novel, general embedding algorithm and a reconstruction method for 5D field theories supporting specific geometries in braneworld models.

Findings

Developed a universal embedding algorithm for 4D geometries into 5D models.

Reconstructed a complete 5D theory supporting a brane-localized Schwarzschild black hole.

Illustrated embedding of a de Sitter brane in braneworld scenarios.

Abstract

We develop a general algorithm that enables the consistent embedding of any four-dimensional static and spherically symmetric geometry into any five-dimensional single-brane braneworld model, characterized by an injective and nonsingular warp factor. Furthermore, we supplement the algorithm by introducing a method that allows one to, in principle, reconstruct 5D field theories that support the aforementioned geometries. This approach is based on a conformal transformation of the metric with the conformal factor being identified with the warp factor of the bulk geometry. The reconstructed theories depend solely on the induced brane geometry, since the warp factor is model-independently represented by a scalar field in the Lagrangian density. As a first application of our reconstruction method, we present for the first time a complete theory that supports the five-dimensional brane-localized extension of the Schwarzschild black hole, for any warp factor. The same method is subsequently utilized to illustrate the process of coherently embedding a de Sitter brane in braneworld models.