Born-Infeld extension of Lovelock brane gravity

TL;DR

This paper introduces a Born-Infeld type theory for p-branes that incorporates Lovelock invariants, depending on the brane's geometry, and explores its properties including Weyl invariance and second-order nature.

Contribution

It develops a novel Born-Infeld extension of Lovelock brane gravity, considering embedding functions as fields and analyzing its geometric and invariance properties.

Findings

The model depends on intrinsic and extrinsic geometries.

It remains a second-order theory despite complex invariants.

Weyl invariance can be achieved with auxiliary fields.

Abstract

We present a Born-Infeld type theory to describe the evolution of p-branes propagating in an N = (p+2)-dimensional Minkowski spacetime. The expansion of the BI-type volume element gives rise to the (p+1) Lovelock brane invariants associated with the worldvolume swept out by the brane. Contrary to the Lovelock theory in gravity, the number of Lovelock brane Lagrangians differs in this case, depending on the dimension of the worldvolume as a consequence that we consider the embedding functions, instead of the metric, as the field variables. This model depends on the intrinsic and the extrinsic geometries of the worldvolume and in consequence is a second-order theory as shown in the main text. A classically equivalent action is discussed and we comment on its Weyl invariance in any dimension which naturally requires the introduction of some auxiliary fields.