Noether Currents for Bosonic Branes

TL;DR

This paper analyzes conservation laws for relativistic bosonic branes in Minkowski space, deriving general expressions for momenta, exploring perturbations, and examining boundary term subtleties in higher-order theories.

Contribution

It provides a unified geometrical framework for conservation laws of bosonic branes with actions depending on extrinsic curvature, including higher-order theories and boundary considerations.

Findings

Derived general expressions for linear and angular momentum.

Explored perturbation theory and solutions with zero energy-momentum.

Analyzed boundary term effects in brane Einstein-Hilbert action.

Abstract

We consider a relativistic brane propagating in Minkowski spacetime described by any action which is local in its worldvolume geometry. We examine the conservation laws associated with the Poincar\'e symmetry of the background from a worldvolume geometrical point of the view. These laws are exploited to explore the structure of the equations of motion. General expressions are provided for both the linear and angular momentum for any action depending on the worldvolume extrinsic curvature. The conservation laws are examined in perturbation theory. It is shown how non-trivial solutions with vanishing energy-momentum can be constructed in higher order theories. Finally, subtleties associated with boundary terms are examined in the context of the brane Einstein-Hilbert action.