I'm sure if the bump was in the right place, it would probably be described as "arch support" but it hit me flat-out wrong and it was hard with no give so there was no chance of the shoe working out.  They managed to be slightly frumpier looking in real life too.  The footbed of the shoe didn't have a lot of cushioning so would probably be supportive but might make your feet sore after a long time.  I wouldn't know though because I only had them on for a minute since they were so uncomfortable.