How do I stop myself from cheating?

I've been with my girlfriend now for almost fifteen years, everything has been going fantastic and I love her, but recently I met another girl and I've found myself falling for her.

I think about her all the time and when we meet up I just sit and think about how much I want to kiss her. Is it possible to be in love with more than one person?

I feel like I'm cheating on my girlfriend even though I've never done anything with this other girl. I just can't get her out of my head