Miguel Cruz, Efraín Rojas
We present a Born-Infeld type model to describe the evolution of p-dimensional branes propagating in a flat Minkowski spacetime which, when expanded explicitly, it gives rise to a finite series involving (p+1) geometrical terms that are related to the Lovelock brane invariants. This model is a second-order volume element that depends on the intrinsic and the extrinsic geometry of the worldvolume swept out by the brane, and it can be regarded as a deformation of the minimal volume element. The field equations are of second-order and we express these in terms of conserved brane tensors. Contrary to the Lovelock theory in gravity, the number of Lovelock brane Lagrangians differs in this case, and it only depends on the dimension of the worldvolume, reflecting the fact that the embedding functions are the field variables instead of the metric. Moreover, we also provide a number of classically equivalent actions for this BI type action and discuss their Weyl invariance in any dimension which naturally requires the introduction of some auxiliary fields.
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http://arxiv.org/abs/1212.1704
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