Our Universe might be a hologram...
That is an oversimplification of something that is otherwise pretty interesting. See, the paper never makes the claim that we live in a hologram (not that it would really mean anything, other than we need to readjust quantum theories and calculations slightly). The whole thing was a proof that shows that quantum gravitation theories can apply to flat spaces instead of just those with negative curvature. Also, we have proof that the universe has three macro-spatial dimensions: Gravity (and the electromagnetic force). in fact, it was proved back in the 1600s, because of Newton. Well, kinda. The proof is that the force of gravity drops off per the square of the distance calculated. The reason for this is calculus based on the spheres and areas of them that you measure. Imagine a sphere around an object you're measuring the force of gravity around. The amount of "force energy" is going to be the same (think charge for charged particles, the charge inside an ever growing sphere around a point charge in empty space is going to remain constant, so there's the same "gravitational charge" inside a similar sphere with mass), so when you measure the force at a distance away, you're measuring the amount of force that's left after the rest has been spread out over the entire area of the sphere. Area of the sphere, you may note, is based on the
square of the radius of the sphere. Each force equation has been found to have a "force charge" (charge for E+M, mass for gravity, each with constants, which I'll talk about more later) over a square of the distance from the point of concentration of the "force charge". This means the force is inversely proportional to the square of the distance, exactly what you'd expect from a three macro-dimensional space: the force is proportional to the area of the sphere. In fact, this can ONLY happen with a 3+ dimensional space, and a force that only acts in three dimensions.
Now, about those constants. One of the odd things about gravity (re: freaking bizarre) is that it is so incredibly weak. If gravity had a base power of '1', the same "force charge" but with the weak nuclear force would have a base power of 10^27, with electromagnetic would be 10^28, and strong nuclear would be 10^30. That means that gravity is about 1000000000000000000000000000 times weaker than the weakest of the three more reasonable forces. This is one of the things that that paper was using as evidence for gravity being weird, and something being up. Gravity is the force that we just don't know anything about really, and the universe being a hologram is a possible explanation for this. Now, the mention the nuclear forces being two dimensional forces, and that's wrong. One is a two dimensional...kinda...force....thing (weak), and the other is....one? negative one? (strong) It's weird is the point. Quantum physics is weird. The force gets bigger as you pull the two "force charges" away from each other (well, three, because there's three of them....but only one at the same time...kinda...). This is called Quantum Colo(u)r Dynamics, governing the Strong force, and the Weak is electroweak theory. These forces don't act in three dimensions, and only operate on really really small distances (10^-15 m and smaller) inside the nucleus of atoms (strong) and quarks (weak).
So what does that mean about dimensions? Well, the quantum forces (strong and weak) aren't really dimensional. We know exactly what cause them and why they work, but we don't really have a model for them, and the how the work is a mystery. Compare with electromagnetism and gravity, where we know how they work, and as for why, gravity is basically just magic as far as science is concerned, and E+M is photons, but we don't have a super good handle on why it works. But one thing that might explain the discrepancy, is that there is a discrepancy between the dimensional levels of the quantum level and macro level. So the idea behind the theory that that story is on, is that at the quantum level, the universe is 2D, but at the atomic level is goes through a change, and becomes three dimensional. It's not terribly different from Einstein's theory of multiple micro dimensions existing, where the dimension is wrapped up and tiny, and we can't really detect it. That's one of the things that might exist at a quantum level.
