Downvotes do exist, but you need to reach 500 karma to unlock them, or at least that's what the rumours say.

I don't have them, but I have seen comments in the negative, so there must be some truth to it

We do in fact have down votes, you just need 500 (I think?) karma to be able to use it. When you see comments that are not "dead" but are greyed out, they've been downvoted more than they've been upvoted.

Thank you for correcting me, my bad.