Yuya Kusuki was staring at the mathematical seam between two nearly identical universes—two conformal field theories so close they almost touch—when he saw where the dials of nature might really come from. Not from outside, not as arbitrary settings tweaked by a theorist’s hand, but from within the theory itself, woven into its very fabric. Alongside Shota Komatsu of CERN, Marco Meineri of the University of Turin, and Hirosi Ooguri at Caltech, Kusuki has uncovered a profound clue in the decades-long quest to unify quantum mechanics and gravity: what look like free parameters in quantum gravity may in fact emerge from local operators already present in the system.
This isn’t just a technical detail—it’s a resurrection of Einstein’s deepest conviction. A century ago, the physicist insisted that the fundamental laws of nature should contain no arbitrary numbers, no knobs to be tuned from the outside. The universe, he believed, should be self-contained, its constants arising from internal dynamics, not imposed by hand. Now, in a breakthrough published in Physical Review Letters, Kusuki and his collaborators have brought that vision closer to reality by probing the structure of conformal field theories (CFTs), mathematical frameworks where space-time symmetries remain unchanged across scales.
At the heart of their work is the conformal manifold—a smooth landscape of related CFTs connected by continuous parameters. If such a manifold exists, does it require exactly marginal operators, the internal engines that can shift the theory without breaking its symmetry? The team proved, under specific conditions, that it does. By examining the behavior of a conformal interface—the boundary between two nearby CFTs—they showed that as the theories converge, an exactly marginal operator can be reconstructed directly from the displacement operator, a local field that responds to shifts in the interface. This means the parameter isn’t free at all; it’s generated from within.
The implications ripple into quantum gravity through the AdS/CFT correspondence, a powerful duality that links certain CFTs to theories of gravity in anti-de Sitter space. If parameters in the CFT arise from internal operators, then in the gravitational picture, there are no externally adjustable constants—just as Einstein imagined. While the result currently applies only to two-dimensional CFTs, the team is already pushing toward higher dimensions, hoping to show this principle holds across the full landscape of quantum theories.
“This supports the idea that the laws of nature are not set by hand but emerge from the theory itself,” Kusuki said. And if that’s true, we’re not just writing equations—we’re uncovering a universe that tunes itself.