A quick holography puzzle I thought about last night as I was falling asleep:

Imagine we have a non-gravitational quantum field theory in dimensions. It’s some complicated thing that we’d like to understand. How about we do the following – add in gravity, compute stuff, and at the end take . The cool thing is that once we add in gravity, we can use holography (assuming we buy it) to think of our theory as non-gravitational in dimensions; maybe it’s simpler, if we’re able to solve things at infinite coupling! But even cooler: let’s repeat the process in our dimensional theory – add in gravity (with the intention to take in our new lower-dimensional theory), so we go to a non-gravitational theory in dimensions! We can iterate this, and eventually realize that any dimensional QFT can be understood as the infinite-coupling limit (for many couplings) of a 0-dimensional quantum mechanical (e.g., SYK) system!

What goes wrong in the above logic? I can think of two four issues, one two of which might be impossible to bypass.