Second order Lagrangian and symplectic current for gravitationally perturbed Dirac-Goto-Nambu strings and branes

TL;DR

This paper develops a second order Lagrangian framework for analyzing gravitational perturbations of Dirac-Goto-Nambu strings and branes, providing a variational principle and symplectic current useful for conservation laws.

Contribution

It introduces a second order perturbation Lagrangian and symplectic current for gravitationally perturbed strings and branes, extending previous analyses.

Findings

Derived a variational principle from a second order perturbation of the Nambu-Goto action.

Constructed a symplectic current functional relevant for conservation laws.

Extended analysis to arbitrary gauge for strings and branes.

Abstract

We extend a recent analysis of gravitational perturbations on Dirac-Nambu-Goto strings, membranes and higher dimensional branes. In an arbitrary gauge, it is shown that the relevant first order equations governing the displacement vector of the worldsheet and metric perturbation are obtainable from a variational principle whose Lagrangian is constructed as a second order perturbation of the standard Dirac-Goto-Nambu action density. A symplectic current functional is obtained as a by-product that is potentially useful for the derivation of conservation laws in particular circumstances.