It's branes not brains BTW
As I said the whole article reads as like mumbo jumbo to me, a bit like when science magazines try to describe quantum entanglement.
I simply don't get anything that means holographic out of "everything allowed to happen in the bulk space-time of the gravitational theory is encoded on the boundary of that space."
I am not a wordsmith but if I had to try I would go something like this
"The universe in classic physics is described by 3 dimensions and time. Brane models in string theory can use the hidden dimensions of space to project a 3D world onto a normal 2D plane in the same way as computer games do it. Electromagnetic, Strong and weak nuclear forces play out only on the 2D plane while time and gravity play out in all the dimensions but project onto the 2D plane. The 3rd dimension is an illusion and hence this is called a holographic theory".
Hard to work out what boundary is being discussed in that mumbo jumbo. If I had to guess, I think the Brane/other dimensions boundary.
All theories that comply with QM/QFT make a definition of fields that propagate a translationally invariant spacetime. So there are a number of possible boundaries in that definition not just one
Now you have progressed I will give you a more interesting boundary to ponder
Emmy Noether demonstrated that conservation laws are linked to symmetries, specifically the validity of the energy conservation law is equivalent to the time-translational symmetry of the laws of physics. So outside our universe must be somewhere time-translational symmetry doesn't hold
