Gravity, p-branes and a spacetime counterpart of the Higgs effect

TL;DR

The paper demonstrates that p-branes act as Goldstone fields for spacetime diffeomorphisms in gravity, showing they lack local degrees of freedom and discussing implications for the Higgs effect and brane world models.

Contribution

It reveals that p-branes serve as Goldstone fields for spacetime diffeomorphisms and lack local degrees of freedom, extending understanding of gauge invariance in gravity.

Findings

p-brane coordinate functions are Goldstone fields for diffeomorphisms

A p-brane does not carry local degrees of freedom

The work relates to the spacetime Higgs effect and brane world scenarios

Abstract

We point out that the worldvolume coordinate functions $\hat{x}^\mu(\xi)$ of a $p$-brane, treated as an independent object interacting with dynamical gravity, are Goldstone fields for spacetime diffeomorphisms gauge symmetry. The presence of this gauge invariance is exhibited by its associated Noether identity, which expresses that the source equations follow from the gravitational equations. We discuss the spacetime counterpart of the Higgs effect and show that a $p$-brane does not carry any local degrees of freedom, extending early known general relativity features. Our considerations are also relevant for brane world scenarios.