Stuckelberg fields on the effective p-brane

We demonstrate a bijection between reparametrization invariant effective actions for relativistic p-branes in flat target space and effective actions for transverse brane perturbations with nonlinearly realized Poincare symmetry. Starting with an action with nonlinearly realized symmetry, we construct the corresponding reparametrization invariant action by introducing Stuckelberg fields. They combine with the transverse modes to form a Lorentz vector. The manifest Lorentz symmetry of the reparametrization invariant action follows directly from the nonlinearly realized Lorentz symmetry of the initial action in terms of the physical modes.