And little things slipped by the editor, like "By 2016, Poland and Simmons-Duffin had calculated the two main critical exponents of the theory out to their millionth decimal places." That seemed completely crazy--and yep, the linked paper showed 1 part in a million, not a million decimal places. SMBC gets that right.
You may want to take some advice from Peanuts: WRT The Brothers Karamazov--Charlie Brown says, "But don't you get confused by all those long Russian names?" Linus says, "Oh, when I come to one I can't pronounce, I just bleep over it."
Researchers are pushing in all directions. Some are applying the bootstrap to get a handle on an especially symmetric “superconformal” field theory known as the (2,0) theory, which plays a role in string theory and is conjectured to exist in six dimensions. But Simmons-Duffin explained that the effort to explore CFTs will take physicists beyond these special theories. More general quantum field theories like quantum chromodynamics can be derived by starting with a CFT and “flowing” its properties using a mathematical procedure called the renormalization group. “CFTs are kind of like signposts in the landscape of quantum field theories, and renormalization-group flows are like the roads,” Simmons-Duffin said. “So you’ve got to first understand the signposts, and then you can try to describe the roads between them, and in that way you can kind of make a map of the space of theories.”
That's a bit of jargon to go wading through, but can you see what's wrong here? Take this: "the (2,0) theory, which plays a role in string theory and is conjectured to exist in six dimensions" This sounds like a theory in search of an application. (I've tried my hand at that myself--it wound up looking more complicated that what it was supposed to explain.)
String theory, for all its attractive foundation, hasn't produced anything substantial yet, and you know you're really at sea when a theory is just "conjectured" to exist in six dimensions. That doesn't mean this (2,0) research isn't interesting--it probably is--just that the connection to the physical world is likely to be tenuous. At best.
The renormalization theories were developed to handle equations that gave infinities (what is ∞ - ∞ ?). When your equations behave like that it seems like a clear sign that this isn't the optimal way of expressing the problem. Maybe this bootstrapping paradigm can be a way of re-expressing problems--though Simmons-Duffin seems to think renormalization is still going to be there.
One particular physics problem looked as though it lay on a "corner" of the boundary of the space of possible configurations of one kind of bootstrap transformations. That's certainly odd, and worth exploring. But when the amplituhedron gets pulled in as a possible connection, it doesn't exactly increase my enthusiasm for the project. That beast is a highly speculative model that hasn't shown any solid connection to real "electron hits pion" physics. Like another theory mentioned above.
UPDATE: FWIW, Motls likes the ideas. He's a string theorist, and has a little different idea about how well string theory has been doing.