St\"uckelberg Fields on the Effective p-brane

Understand

We demonstrate the one-to-one correspondence between reparametrization invariant effective actions for relativistic p-branes in flat target space and effective actions for transverse brane perturbations with non-linearly realized Poincar\'e symmetry.

• Starting with an action with non-linearly realized symmetry we construct the corresponding reparametrization invariant action by introducing St\"uckelberg 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 non-linearly realized Lorentz symmetry of the initial action in terms of the physical modes.