And, as always with these kinds of papers, everything only works out in ADS space, which has nothing in common with how our own universe works...
If anyone else never heard of the "Anti-de Sitter space" [0] here a short description from Wikipedia:
> In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (1872–1934), professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked together closely in Leiden in the 1920s on the spacetime structure of the universe.
Sadly this is so far outside of my level of understanding that I still don't have a clue.
Would love an ELI5.
[0]: https://en.wikipedia.org/wiki/Anti-de_Sitter_space?wprov=sfl...
The analogs of these things in higher dimensions, and where one of the directions is time, are important in general relativity. The analog of the plane is called “flat space” or “Minkowski space”. The analog of the sphere is “de Sitter space”. Finally, the analog of the saddle is “anti-de Sitter space” (usually abbreviated AdS, with a lowercase d). It’s a bit of an odd space in a lot of ways. When you look at what space looks like at any given time, it’s a bit like M.C. Escher’s “Angels and Devils”.
Surprisingly, Anti-de Sitter space is the easiest space to understand quantum aspects of gravity in. That’s because anti-de Sitter space is curved in such a way that the complicated stuff can be neatly separated from the easy stuff. You can start from something you understand well and turn on the complexity piece by piece. Roughly speaking it’s because the gravitational stuff becomes less important as you go farther and farther away from any matter you’re considering, in a way which is even faster than this happens in flat space or de Sitter space. It turns out that we can exactly understand everything in this gravitational theory by mapping the physics one-to-one to a nongravitational model which we understand really well. There’s a lot of evidence that the map works perfectly. This is called the AdS/CFT correspondence. A lot of work goes into testing the correspondence and attempting to prove it, and this is a big research area.
de Sitter space doesn’t have the same desirable properties. Nevertheless there has been great progress in understanding quantum properties of de Sitter in the last year [0]. These results would not have been possible without understanding AdS first.
Flat space quantum gravity remains challenging, although again some progress has been made recently too [1].
[0] arxiv:2110.14670
[1] arxiv:1905.09809 and many others
So there is flat space, de Sitter space, and Anti-de Sitter space, do we know which one most closely resembles the world we observe?
The quantity that measures this is called the cosmological constant. It’s zero in flat space, positive in de Sitter and negative in anti-de Sitter. It turns out from measurements that our cosmological constant is positive but outrageously small, tiny compared to anything else we know about in physics. This is puzzling because we would love to relate it to something we understand already but it’s hard to arrive at a result so small working with quantities that are considerably larger. So there’s an interesting open question about why it is what it is.