Gravitating p-Branes

TL;DR

This paper constructs a gravitational action for p-branes with broken Poincare symmetries using coset methods, revealing a coupled system of massive gauge fields and gravity, and applies it to a vortex in a 6D model.

Contribution

It introduces a new invariant action for gravitating p-branes with broken symmetries, including massive gauge fields and their coupling to gravity.

Findings

Derived an ISO(1,p+N) invariant Einstein-Hilbert type action.

Identified massive gauge fields corresponding to broken symmetries.

Applied the formalism to a vortex in a 6D Abelian Higgs model.

Abstract

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local Poincare symmetries of D dimensional space-time due to the embedding of a p-brane with codimension N=D-p-1. The resulting action is an ISO(1,p+N) invariant form of the Einstein-Hilbert action, which, in addition to the gravitational vielbein, also includes N massive gauge fields corresponding to the broken space translation symmetries which together carry the fundamental representation of the unbroken SO(N) gauge symmetry and an SO(N) Yang-Mills field localized on the brane. The long wavelength dynamics of the gravitating p-brane is the same as the action of an SO(N) vector massive Proca field and a non-Abelian SO(N) Yang-Mills field all coupled to gravity in d=(1+p) dimensional space-time. The general results are specialized to determine the effective action for the gravitating vortex solution in the D=6 Abelian Higgs-Kibble model.