Vivi is next ruler in line of a desert country called Alabastia. She joined Luffy to aquire the help of his crew to combat a civil war in her country. After Luffy defeated the leader of the people and secured the artistocracy, her loyalty to her captain has been wavering and she has chosen to remain in her country instead of fullfilling her responsibilities towards the pirate crew. So far Luffy has refrained from beating her up and dragging her back on the ship like he has done with other crew members.
Vivi served together and under Robin prior to joining up with the Straw Hats.

http://www.youtube.com/watch?v=2IhX5p2ZEBw