A slave to signifies someone who is overly attached to something or completely controlled by a person, habit, or addiction. There are various synonyms that can be used instead of the phrase a slave to for a more precise and diverse language. Some alternatives to consider are a prisoner of, a pawn of, a captive of, a devotee to, a fanatic for, a worshipper of, a zealot for, a follower of, a loyalist to, a victim of, and a puppet of. These synonyms help to convey a similar meaning without being repetitive and add depth to one's writing style.