You may have heard that Shame is a movie about sex. It's really not. It's a movie about addiction.

Shame drops in on the life of Brandon Sullivan, a 30-something New Yorker with an office job, an apartment in a brand-new building in the West 30s, and a compulsive inability to maintain sexual continence, which troubles him deeply. The movie concerns Brandon's relationship with his younger sister, Sissy, an alcoholic up-and-coming singer with a depressive streak. Sissy comes back to the city from a spell in Los Angeles and fetches up at Brandon's apartment, and for whatever reason, he can't quite manage to roust her. Over the next days, they fight, stumble upon each other's hidden selves, and maybe, just maybe, find some kind of resolution.

That the fine Irish actor Michael Fassbender, who plays Brandon, and the equally skilled English actress Carey Mulligan, who plays Sissy, don't look like siblings doesn't actually hurt the film; Fassbender's face is all hard planes and sharp angles, while Mulligan's is all curves, with her button nose and Cupid's bow mouth. Their respective physicalities echo the emotional gulf between them: Sissy is messy, whether blubbering on the phone to an absent boyfriend (her desperate plea, "But I love you! I love you! I love you!" is heartbreaking) or standing too close to the edge of the subway platform. She's also needy, always pressing Brandon for some sign of warmth, which is just one of the many emotional responses her brother seems constitutionally ill-equipped to give. Brandon, for his part, is cold and controlled. He deletes, un-played, the voicemails left by women he's gone on dates with, and his usual first response to Sissy's acting out — such as when she sleeps with Brandon's boss, in Brandon's bed — is to clench his jaw and go for a long run around Midtown.

The movie is excruciatingly slow-paced. Director Steve McQueen lingers on scenes until they reach, and surpass, emotional breaking point. When Sissy sings the world's most melancholy cover of "New York, New York," at the nightclub at the top of the Standard Hotel, which is called the Boom Boom Room, McQueen gives us the whole song. It's punishing. Shots of Brandon padding around his apartment — urinating, tooth-brushing, message-deleting — in the nude go on for what seems to be forever. Brandon is getting pegged in reviews as a Wall Streeter, but I don't know many men who turn up to their jobs in finance wearing sweaters, khakis, and collared shirts without a tie. His personality is as indeterminate as his job: when he tells a woman on a date that his longest relationship lasted four months, she tells him, "You have to really try, to commit." He replies, sort of sheepishly, "I did."

Brandon is isolated by his addiction. He takes regular masturbation breaks in his workplace bathroom. He orders prostitutes at night, sometimes several. His laptop at home is enlivened by pay-per-minute camgirls who know him by name; his desktop at work is so rotten with porn that IT support takes it away. ("Do you think it was your intern?" asks the boss.) Brandon has sex like an alcoholic drinks: compulsively, indiscriminately, and for the sake of release rather than for intimacy, pleasure, or human feeling. In one early scene, Brandon is out drinking at a bar with colleagues when his boss starts hitting on a beautiful woman in a suit. Hitting on her quite badly. The boss has recently claimed to be "an expert in attention to detail" when the woman closes her eyes and says, "Blue or green"; boss guesses wrong. At that moment, Brandon steps up to the bar, and the woman turns to him, eyes closed. "Brown," Brandon says, before she can even ask. He is simply too good, too practiced, a seducer to derive any enjoyment from his seductions. Sex, when it comes to him, comes predictably and without the element of surprise that might be a precursor to feeling actual happiness. Sex is a disappointment, because for it to come so readily confirms, to Brandon, that sex is essentially worthless. Which in turn confirms Brandon himself as worthless — shameful — for seeking it out. He fucks the woman in the suit against the pillar of a highway overpass.

The interesting thing is, Shame is not exactly a date movie — but it won't kill a healthy carnal appetite, either. Brandon doesn't have sex like normal people. Your idea of self-hating sex might be sleeping with that dude who doesn't always text you back (again): Brandon's entire sexuality, in contrast, seems to be rooted in and an expression of self-hatred. Every single one of the (many) times Brandon is shown checking out a woman, you can practically feel the rise of the old, familiar self-loathing (and the hardening of his cock). Fassbender is just that good in the role. When Sissy crawls into Brandon's bed one night, to snuggle and to apologize for something, he tells her to get back to the couch — first curtly, and then with real anger. One has to wonder to what extent that's because he's actually upset with her, and to what extent it's because he doesn't know if he can entirely trust himself.

It's hinted, but never explained, that Brandon and Sissy share some traumatic history — perhaps of childhood abuse, or some more ordinary psychological ill, like divorce or parental abandonment. "We aren't bad people," Sissy tells him at a climactic moment, tearfully as ever. "We just come from a bad place." They moved from Ireland to New Jersey when Brandon was aged 12, and when Sissy goads him into an actual fight, they yell at each other with their Irish accents. Just like real people of foreign heritage, whose old speech patterns resurface at times of high emotion.

Shame is American Psycho, minus the satire, and with fucking instead of murder. When Brandon tells a stranger in a bar what he'd like to do to her body — eat her pussy, taste her, put his tongue inside her — he sounds like a killer describing what he's going to do to his latest victim. Later that night, Brandon goes to a gay sex club, and gets a blow job from the guy he's been making eyes with from across the street outside. Depicting a straight character seeking out a homosexual encounter as a sex addict's "rock bottom" is the film's one sour note; I found it politically problematic bordering on homophobic, and frankly a cheap move from an otherwise highly subtle and carefully observed story of human relationships, and human failure. It is sort of made better by the fact that there is another, much more devastating, bottom to come.

One of the best things about Shame — aside from Fassbender's and Mulligan's spellbinding performances — is its portrait of the city of New York. It looks like New York actually looks. The subway is as filthy as Brandon's computer, and the scenes of 20- and 30-somethings mingling at various interchangeable bars and nightclubs seem like the most soulless of mating rituals. This New York is about getting into the right kind of restaurant, and it's also about getting into a bar fight and having to ride the subway home, drunk and bleeding, at 4 a.m. And it's about money. (I cringed at the thought of the bill when Brandon, his boss, and Sissy ordered two martinis, a whiskey, and a bottle of champagne — with table service — at the Boom Boom Room, an establishment where a vodka-and-soda will set you back $18. Brandon also fucks a prostitute at the Standard; you could probably write a whole essay on Shame and Balazs hotels.) Mercifully, no character ever just up and starts talking about how much they love New York! The absence of the usual city-that-never-sleeps claptrap is bracing and welcome. In Shame, New York is just a place, but it's at least the place you recognize, not some Disneyfied Darren Star confection where everybody takes cabs and wears $800 shoes.

The film ends with Brandon on the cusp of a decision — we don't know whether he's going to do the thing he wants to do, or the thing he wants to want to do. There is little in the movie that indicates we should be hopeful for Brandon. But somehow, a couple days after seeing it, I am. Perhaps. Just a little.