It might not be connected to your other personas, but there's still someone at facebook who can piece together what apps and sites you use that require facebook logins, and potentially abuse that data.
Chances are it is connected to the other personas and facebook has a more complete than you think profile, heck they don't even need you to be registered to have a profile on you, from being in registered people's addressbook to going to web page featuring a facebook button they can piece together a profile.
