Lovelock type brane gravity from a minimal surface perspective

TL;DR

This paper investigates the geometric foundations of Lovelock-type brane gravity, revealing its natural emergence from a shifted volume-based DNG action and exploring its connections to disformal transformations and scalar-tensor theories.

Contribution

It establishes a geometric framework linking Lovelock brane gravity to minimal surface theory and Dirac-Nambu-Goto actions, enabling new insights into its structure and potential quantization.

Findings

Lovelock brane gravity arises from a volume element shifted along the normal vector.

The geometry depends on fundamental forms and conserved tensors.

Disformal transformations relate Lovelock brane gravity to scalar-tensor theories.

Abstract

We explore the correspondence between the parallel surfaces framework, and the minimal surfaces framework, to uncover and apply new aspects of the geometrical and mechanical content behind the so-called Lovelock-type brane gravity (LBG). We show how this type of brane gravity emerges naturally from a Dirac-Nambu-Goto (DNG) action functional built up from the volume element associated with a world volume shifted a distance $\alpha$ along the normal vector of a germinal world volume, and provide all known geometric structures for such a theory. Our development highlights the dependence of the geometry for the displaced world volume on the fundamental forms, as well as on certain conserved tensors, defined on the outset world volume. Based on this, LBG represents a natural and elegant generalization of the DNG theory to higher dimensions. Moreover, our development allows for exploring disformal transformations in Lovelock brane gravity and analyzing their relations with scalar-tensor theories defined on the brane trajectory. Likewise, this geometrical correspondence would enable us to establish contact with tractable Hamiltonian approximations for this brane gravity theory, by exploiting the linkage with a DNG model, and thus start building a suitable quantum version.