The answers reflect the diversity of thought on this, however @eenbeetje answer is correct. Both can be used, but "slowly" is, shall we say, less controversial because it is the conventional form of the adverb. But the link is @eenbeetje answer is an excellent one to learn about flat adverbs. As I commented there, they are considerably more common in the US than in Britain.
However, I did want to point out a great example of this, and that is that famous Apple slogan of "Think Different". I think it is one of the greatest slogans of all time because it is this self referential thing. You read it and think: "Hey, shouldn't that be 'think differently'" then you realize that people do say "think different', and it is a bit off, a bit unconventional, a bit edgy (and, also correct.) The wording itself, and how you react to it conveys exactly the ideas that Apple wanted to convey to you about their products. "Different", "edgy", "coloring outside the lines", "the regular folks think it is wrong, but they just aren't smart enough to know that it is in fact correct."
How you can convey all that feeling and reaction in just two words is quite remarkable. Whoever wrote it is a genius.