We present near-infrared integral-field spectroscopic observations targeting H$alpha$ in eight sub-millimeter galaxies (SMGs) at $z$=1.3-2.5 using VLT/SINFONI, obtaining significant detections for six of them. The star formation rates derived from the H$alpha$ emission are $sim$100 M$_odot$yr$^{-1}$, which account for only $sim$ 20-30% of the infrared-derived values, thus suggesting that these systems are very dusty. Two of these systems present [NII]/H$alpha$ ratios indicative of the presence of an Active Galactic Nucleus (AGN). We mapped the spatial distribution and kinematics of the star forming regions in these galaxies on kpc-scales. In general, the H$alpha$ morphologies tend to be highly irregular and/or clumpy, showing spatial extents of $sim$3-11~kpc. We find evidence for significant spatial offsets, of $sim$0.1-0.4$$ or 1.2-3.4 kpc, between the H$alpha$ and the continuum emission in three of the sources. Performing a kinemetry analysis we conclude that the majority of the sample is not consistent with disk-like rotation-dominated kinematics. Instead, they tend to show irregular and/or clumpy and turbulent velocity and velocity dispersion fields. This can be interpreted as evidence for scenario in which these extreme star formation episodes are triggered by galaxy-galaxy interactions and major mergers. In contrast to recent results for SMGs, these sources appear to follow the same relations between gas and star forming rate densities as less luminous and/or normal star forming galaxies.
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