She was 26, raised in Minnesota, the daughter of a World War II veteran and a Norwegian immigrant. She'd already published a poem in a leading journal and was immersed in her dissertation on Charles Dickens at Columbia University. He was 34, an aspiring writer who'd packed off for Paris following his graduation from Columbia but had circled back to the frenzy of New York City.

On the rebound from a failed first marriage, he was translating French writers and mulling the complex tensions of the Jewish-American experience, grist for the imagination. They'd fallen in love and had just rented their first apartment together in Brooklyn: not the polished bohemian haven of today, but the Brooklyn of a generation ago, roiled by petty crime, crack vials and gutter-trash, the necessity of neighbour escorts to and from the subway. A borough overshadowed by its glittering sibling across the East River.

She was standing on the stairs in their apartment, he below her. He grabbed her arm and leaned forward, lips puckered. But first he asked, in a gruff voice, 'Beckett or Burroughs?'
'Beckett!' she almost shouted. Their lips met, and they kissed and kissed, sealing the deal.

Nearly four decades later, when you visit Siri Hustvedt and Paul Auster in their Park Slope home, you still feel the gauzy-lens romance of their early days, but also the 'ever-mutating' (Hustvedt's term) nature of a steely, enduring marriage and literary partnership, minds and hearts entwined, waltzing to their internal harmonies and dissonances. Hustvedt, tall and blonde, elegant and commanding; Auster, boisterous and broad-shouldered, hinting at his baseball-player youth.

Over the course of their relationship they've brought out a total of 51 books that range across genres – literary fiction, memoir, crime noir, critical essays – along with a robust serving of translations and screenplays. Though they spend their mornings and afternoons apart – Hustvedt's study is on the top floor of their house, Auster's tucked in the basement – they share drafts with each other in the evenings, benefitting from a mutual familiarity with their material. 'I give Paul my manuscripts, chapter by chapter. He inevitably puts his finger on the soft spots,' Hustvedt says. Auster asserts that 'Siri's an astute reader; I rarely fight her suggestions. If I'm going off track, she'll pull me back.'

Their tastes in books, art, and film are, in Auster's phrase, 'congruent but not identical', which could also describe their current work. He is best known for his fiction oeuvre: City of Glass (the graphic novel of which has just been re-issued), Leviathan, Mr Vertigo, and now 4 3 2 1, a panoramic epic that explores post-war America through four versions of a single character, Archie Ferguson, born (like Auster) in 1947 New Jersey.

Auster teases out common threads among the Archies but also myriad variations, sly and jazzy, a magician's sleight of hand. Also an acclaimed fiction writer – her last novel, The Blazing World was longlisted for the Man Booker prize and won the 2015 Los Angeles Times prize for fiction – Hustvedt has increasingly moved toward neurobiology and psychology, their influence on gender and behaviour and connections to art and literature.

Her collection of essays, A Woman Looking at Men Looking at Women, brims with erudition as it roams from swaggering, macho painters such as Pablo Picasso and Jackson Pollock to The Delusions of Certainty, a cerebral tour de force that leaps from Descartes to Darwin to Steven Pinker to Simone Weil.

But the Hustvedt-Auster marriage isn't all about slipping the surly bonds of earth. Like many fellow authors, they've stepped up to the challenges posed by the surprising election of Donald Trump to the presidency, which revealed deep fault lines in American culture. Throughout the gruelling 2016 campaign, Hustvedt recoiled from Trump's 'absolutely striking' misogynistic statements. She dove into the broader political crisis – 'white populism and its emotional demons' – with new pieces for Slate, The Guardian, and Le Monde, all cast with a feminist slant.

Auster's new novel grapples with the eternal flame of racism; in the run-up to 4 3 2 1's British publication, he conducted an interview with Newsnight. He's also taking a more active role in the influential writers' association, PEN International. But he insists that 'there's no obligation' for writers to be political activists. 'Writing is art; as a form, the novel offers the particular experiences of humans. Two strangers can meet on the page in the most intimate way,' he observes, and then inadvertently shifts into third-person: 'Paul and Siri are citizens who write!'

Hustvedt concurs: 'The novel must take place inside an aesthetic frame, one that makes it possible for readers to travel from their own experiences safely: Dostoevsky's Crime and Punishment is the archetypal example.'

Both Hustvedt and Auster note an aggressive spirit of activism in the streets, kindled by the shock of Trump and the complacency that crept in during the Obama years. 'Writing a novel is a democratic process that values all lives,' Hustvedt says, hand curving into a fist: in that sense all novels are de facto political. But the strange, and strained, political climate in the United States has left the couple more puzzled than pessimistic.

Both concede that precedents and norms have unravelled; but as of this interview there's no compelling evidence that laws have been broken. Hustvedt confesses to dark moments strobed by glimmers of optimism. 'We're accustomed to thinking of our institutions as strong granite buildings,' Auster says. 'We're about to find out whether they're just shells.' He nods, mouth a pursed line. 'We'll know more after the 2018 elections.'

For now, the personal, er, trumps the political. You can hear the tone of pride when Auster and Hustvedt mention their daughter, Sophie, a 30-year-old singer-songwriter who lives in Manhattan's Tribeca neighbourhood. From an early age Sophie showed creative tendencies, drawn to music.

As a teenager she cut the first of her three albums. 'She's one of us, a real artist, she writes songs and performs,' notes Auster. 'We admire and respect her.' Unlike many artists, though, Sophie has always seemed comfortable in her own skin: 'she was constantly in good spirits, even as a child.'

Four decades in the making, Hustvedt and Auster's literary partnership will come to Edinburgh for the Book Festival. They've been invited before but for various reasons have been unable to attend
… until now.

Auster turned 70 earlier this year and 2017 marks the festival's 70th anniversary. 'How could we say no?' he asks rhetorically, arms half-open, filling his Brooklyn kitchen with warmth and brio. The good news for readers on both sides of the Atlantic: Hustvedt and Auster are at the height of their powers, and we should all look forward to more essential fiction and non-fiction that provokes debate and strips away feeling. Books that illuminate and delight even as they candidly speak truth to power.

Paul Auster at 70, King's Theatre, Leven Street, 14 Aug, 6.30pm, £15 (£12).
Siri Hustvedt, 17 Aug, 1.30pm, £12 (£10); 5.30pm (Amnesty International event), free; 18 Aug (with Elif Shafak), 3.15pm, £12 (£10).
Paul Auster, 18 Aug, 8.15pm, £12 (£10).
Events at Charlotte Square Gardens, unless stated.