It exists as an ideal. This ideal is impossible to achieve simply because it is so subjective.
The Matrix (of all things) had a pretty interesting take on this: there was a "Perfect World" where there was no crime, no poverty, no hunger...and yet people rejected it. People needed an imperfect world in order to strive to make things better. Maybe that's where human perfection lies, in the constant need to improve.
Also, and this may be a little shocking, but an episode of Duckman title "Gripes of Wrath" had a similar take on this as well. There was a supercomputer which created a perfect world. But Duckman couldn't stand it. He said, " You made things worse when you made them better! I mean, I liked having a lot of free time, but I hated not having anything to do. Don't you see, things were good when they were bad, and they got bad when they were good. People aren't happy unless they're unhappy. " Why I remember this, I have no idea...and this has to be the first time anyone has brought up Duckman for a philosophical topic.
Anywho, it does not exist in the physical world because it cannot exist. The same reason infinity cannot exist in the real world (impossibly big may be close enough for most people) because it is an ideal. However, it DOES exist in the minds of men (and women). So does that make it real?