  Transport in suspended metallic single wall carbon nanotubes in the presence
of strong electron-electron interaction is investigated. We consider a tube of
finite length and discuss the effects of the coupling of the electrons to the
deformation potential associated to the acoustic stretching and breathing
modes. Treating the interacting electrons within the framework of the Luttinger
liquid model, the low-energy spectrum of the coupled electron-phonon system is
evaluated. The discreteness of the spectrum is reflected in the differential
conductance which, as a function of the applied bias voltage, exhibits three
distinct families of peaks. The height of the phonon-assisted peaks is very
sensitive to the parameters. The phonon peaks are best observed when the system
is close to the Wentzel-Bardeen singularity.
