# Field-Theoretical Formulation of Regge-Teitelboim Gravity

## TL;DR

This paper develops a field-theoretical formulation of Regge-Teitelboim gravity, treating spacetime as a surface embedded in higher-dimensional Minkowski space, and explores its symmetries and Lagrangian structure.

## Contribution

It introduces a novel field theory approach to Regge-Teitelboim gravity, framing spacetime as a surface defined by constant-value fields.

## Key findings

- Symmetry properties of the theory are analyzed.
- Possible structures of the Lagrangian are discussed.
- The formulation provides new insights into embedding-based gravity models.

## Abstract

Theory of gravity is considered in the Regge-Teitelboim approach in which the pseudo-Riemannian space is treated as a surface isometrically embedded in an ambient Minkowski space of higher dimension. This approach is formulated in terms of a field theory in which the original pseudo-Rimannian space is defined by the field constant-value surfaces. The symmetry properties of the proposed theory are investigated, and possible structure of the field-theoretical Lagrangian is discussed.