By Jeff Labrecque
Updated January 30, 2014 at 03:09 PM EST

In Enemy, Jake Gyllenhaal has to share the screen with an actor every bit as handsome and talented as himself. He plays a college professor who becomes obsessed with tracking down the minor actor he spots in a movie that looks remarkably like him. The professor has an attractive girlfriend, the actor is about to become a father, but when their worlds collide, neither man will ever be the same.

Based on The Double by Nobel Prize-winning author Jose Saramago, Enemy is the second collaboration between Gyllenhaal and French-Canadian director Denis Villeneuve (though they filmed Enemy before making Prisoners). “The movie was a kind of cinematic laboratory for Jake and I,” says Villeneuve. “Jake is a very versatile and very creative actor, and it wasn’t very difficult to create two characters. He really fell in love with this idea of exploring this character, a man struggling with intimacy. It was something that we had a lot of ideas about, both of us. It’s a subject that really inspired him. This whole project is borne in that relationship, the bonding between Jake and I.”

When the film premiered at last fall’s Toronto Film Festival, critics applauded and everyone was gobsmacked by the film’s twisty, existential ending. “The movie is a bit mind-bugging and it’s constructed as a spiral,” says the filmmaker. “It’s a bit normal that people are a bit confused, but you’re supposed to experience pleasure with that confusion, not frustration. It was designed to be very playful, meaning it’s really a movie like some of the films that I liked when I was young, like the Twilight Zone, for instance, and some Kubrick movies that created inside of me that kind of strong vertigo feeling.”

The poster for the film is an equally disorienting visual that ignores its leading man’s celebrity. “Enemy for me is really an artistic piece,” says Villeneuve. “It was done with no compromises, a real act of cinema. And I think the poster reflects that idea, that it’s about exploration of identity. Sometimes, it’s very healthy to make cinema with just art in mind and you don’t think about the box-office. What I love about [the distributor] A24 and the poster they came up with is that it totally reflects that.”

Enemy, which co-stars Mélanie Laurent, Isabella Rosellini and Sarah Gadon, premieres on DirecTV on Feb. 6 and opens in theaters March 14.