The holographic principle is often compared to a hologram: all the information about a volume is encoded on a flat surface. In physics, this means that three-dimensional spacetime with gravity could be equivalent to a two-dimensional theory without gravity — a so-called conformal field theory (CFT).

A few years ago, a bold idea emerged: what if three-dimensional gravity is not a single CFT but a whole 'orchestra' of many CFTs, averaged in a special way? This was dubbed ensemble holography. The authors of the new paper tested this hypothesis for a specific model — the doubled Virasoro topological field theory. They studied the simplest case: a space shaped like a bagel (torus) with one hole. It turned out that if you take only standard boundary conditions, any averaging yields a dull result — all members of the ensemble become identical.

Technically, the proof relies on elegant mathematics: transformations of the torus shape (the so-called S and T) are identified with the even Weil representation of the metaplectic group. Then the Cowling–Steger theorem on lattices is applied. The conclusion is harsh: in the studied sector and under ordinary boundary conditions, the ensemble interpretation fails. But the authors emphasize: this does not completely close the idea. What failed is the simplest realization. There remain loopholes — more complex topologies, additional sectors, or even non-standard boundary conditions.

The upshot resembles a detective story: one of the most intriguing hypotheses in modern theoretical physics underwent a rigorous test on the simplest example and failed. But the investigation continues — ahead lie more complex scenarios where ensemble holography might still prove itself.