The IRLB8721PbF FET needs more than 2.5V gate to source voltage to handle more than 10A. The Arduino output needs to be 5V. Go to http://www.tme.eu/en/Document/b69003e9a3061f81b201d4c8f0c01a07/irlb8721pbf.pdf and check out fig.3.
Try connecting your FET gate to your Arduino +V and see what happens.