ClapYo'Hands, no they don't. I've seen unaccompanied teenagers all the time at various shows. I can't speak from personal experience since I wasn't so interested in theatre at that age but I know it's allowed. As long as they're well-behaved, I don't care who's there. In fact, I've witnessed the most problems with the 30 and 40 somethings in terms of texting, talking, etc. (But that's a whole 'nother thread)
Posters here are cautioning that the parent (or whomever is posting this question) may want to consider whether a 14-year-old is mature enough to see a show like BOM by himself. I would tend to agree.
Scratch and claw for every day you're worth!
Make them drag you screaming from life, keep dreaming
You'll live forever here on earth.