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 Feb 2017

www.quantamagazine.org www.quantamagazine.org

pursue this abstraction

Maldacena’s duality, called the “AdS/CFT correspondence,” tied the CFT to a corresponding “antide Sitter space,” which, with its extra dimension, pops out of the conformal system like a hologram.

ArkaniHamed speculates that the polyhedron is related to, or might even encompass, the “amplituhedron,” a geometric object that he and a collaborator discovered in 2013 that encodes the probabilities of different particle collision outcomes — specific examples of correlation functions.

Polyakov initially didn’t believe it. His suspicion, shared by others, was that “maybe this happens because there is some hidden symmetry that we didn’t find yet.”

Uncovering the polyhedral structure representing all possible quantum field theories would, in a sense, unify quark interactions, magnets and all observed and imagined phenomena in a single, inevitable structure

But conformal systems, described by “conformal field theories” (CFTs), are uniform all the way up and down, and this, Polyakov discovered, makes them highly amenable to a bootstrap approach.

Critical exponents corresponding to other wellknown universality classes lie at kinks in other exclusion plots.

Scale symmetry means there are no absolute notions of “near” and “far” in conformal systems;

These critical exponents are clearly independent of either material’s microscopic details, arising instead from something that both systems, and others in their “universality class,” have in common.

What materials at critical points have in common, Polyakov realized, is their symmetries: the set of geometric transformations that leave these systems unchanged. He conjectured that critical materials respect a group of symmetries called “conformal symmetries,” including, most importantly, scale symmetry.

The bootstrap approach
This also sounds a bit like complexity theory at play. What happens when we have some very simple laws and extrapolating them to higher and higher planes gives us the final answer. Naturally there are constraints, but this doesn't sound much different.

Their findings indicate that the set of all quantum field theories forms a unique mathematical structure, one that does indeed pull itself up by its own bootstraps, which means it can be understood on its own terms.
What kind of structure? Group? Ring? Other?

This theory of quark interactions, called quantum chromodynamics, better matched experimental data and soon became one of the three pillars of the reigning Standard Model of particle physics.
