  We present deep mid-infrared spectroscopy with the Spitzer Space Telescope of
13 submillimeter galaxies (SMGs) in the Great Observatories Origins Deep Survey
North (GOODS-N) field. We find strong polycyclic aromatic hydrocarbon (PAH)
emission in all of our targets which allows us to measure mid-IR spectroscopic
redshifts and place constraints on the contribution from star formation and
active galactic nuclei (AGN) activity to the mid-IR emission. In the high
signal-to-noise ratio composite spectrum of SMGs, we find that the hot dust
continuum from an AGN contributes at most 30% of the mid-IR luminosity. We find
that the mid-IR properties of SMGs are distinct from those of 24 micron
-selected ULIRGs at z~2; the former are predominantly dominated by star
formation while the latter are a more heterogeneous sample with many showing
significant AGN activity. We fit the IRS spectrum and the mid-IR to radio
photometry of SMGs with template spectral energy distributions to determine the
best estimate of the total infrared luminosity from star formation. While many
SMGs contain an AGN as evinced by their X-ray properties, our multi-wavelength
analysis shows that the total infrared luminosity, LIR, in SMGs, is dominated
by star formation and not AGN activity. We find that high redshift SMGs lie on
the relation between LIR and LPAH6.2 (or LPAH7.7 or LPAH11.3) that has been
established for local starburst galaxies. This suggests that PAH luminosity can
be used as a proxy for the star formation rate in SMGs. SMGs are consistent
with being a short lived cool phase in a massive merger. Although there appears
to be an AGN present in many SMGs, it does not appear to have become strong
enough to heat the dust and dominate the mid- or far-infrared emission.
