Non-linear Realizations, Goldstone bosons of broken Lorentz rotations and effective actions for p-branes

TL;DR

This paper develops a framework for describing p-branes using non-linear realizations of the Poincare group, deriving the Nambu-Goto action and higher derivative corrections through Maurer-Cartan forms.

Contribution

It introduces a method to construct p-brane effective actions from non-linear realizations, including higher order derivative terms, using Maurer-Cartan forms.

Findings

Derivation of the Nambu-Goto p-brane action from Maurer-Cartan forms.

Phase space analysis confirms the canonical form of the p-brane action.

Construction of higher derivative terms for effective p-brane actions.

Abstract

We consider the non-linear realizations of the Poincare group for p-branes with local subgroup SO(1,p)*SO(D-(p+1)). The Nambu-Goto p-brane action is constructed using the Maurer Cartan forms of the unbroken translations. We perform a throughout phase space analysis of the action and show that it leads to the canonical action of a p-brane. We also construct some higher order derivative terms of the effective p-brane action using the MC forms of the broken Lorentz transformations.