Does Fiction Exist? (ft. Harry Potter)

We all know who Harry Potter is, and can conjure an image of him in our minds. There are specific properties that make a Harry THE Harry (glasses, scar, wand, etc), so it's safe to say that we're all sharing a consistent idea. But do these physical properties mean that Harry Potter EXISTS? Harry Potter doesn't have a physical referent, but the fact that we collectively KNOW Harry Potter (or Hermoine, Ron, or even Batman for that matter), doesn't that mean there's SOME SORT of existence?