St\"uckelberg Fields on the Effective p-brane

TL;DR

This paper establishes a direct correspondence between reparametrization invariant actions for relativistic p-branes and effective actions for transverse perturbations with non-linear Poincaré symmetry, using St"uckelberg fields.

Contribution

It introduces a method to construct reparametrization invariant actions from non-linearly symmetric actions via St"uckelberg fields, clarifying the symmetry structure.

Findings

Demonstrates the one-to-one correspondence between the two types of actions.

Shows how St"uckelberg fields combine with transverse modes to form Lorentz vectors.

Reveals the manifest Lorentz symmetry from non-linear realizations.

Abstract

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.