What "investigation" consumes Chillingworth?

Chillingworth is one twisted guy. He is obsessed in finding out the truth about Pearls father. He has a pretty good hunch it is Dimmesdale but enjoys torturing Dimmesdale until he gets a full confession from him. I think there is a part of Chillingworth that does not want a full confession lest he lose control over his creepy relationship with Dimmesdale.