7

I start with the Large $N$ QCD paper by 't Hooft. When 't Hooft published his paper on Large $N$ QCD it was clear why the string theory of hadrons due to Gabriele Veneziano could make sense. But at the same time, it was an end to strings as fundamental entities responsible for strong nuclear force. In fact, it turned out that the large $N$ QCD gives rise to Flux tubes and turned out as an effective field theory of QCD.

My question is, why don't we interpret AdS/CFT in the same manner, in the sense that the large $N$ limit of super Yang-Mills theory gives rise to a Stringy picture that is by definition only an effective field theory of the Super Yang-Mills in the large $N$ limit?

The fact that such duality is proven in that particular limit and not for arbitrary finite $N$ is the core of my question.

Bastam Tajik
  • 1,310

1 Answers1

8

If string theory were really a UV completion of gravity then it would make a prediction for quantum gravity S-matrix elements when Newton's constant is large. But this cannot be done with the perturbative formulation based on the genus expansion. Rather, the main way people have of computing these large $G$ observables is to "believe the duality" and then do a small $N$ calculation in $\mathcal{N} = 4$ Super Yang-Mills using field theory methods (Feynman diagrams, integrability, bootstrap, localization and maybe lattice).

So for now, $\mathcal{N} = 4$ Super Yang-Mills with small $N$ defines what we mean by strongly coupled type IIB string theory around $AdS_5 \times S^5$. I.e. it admits a limit which agrees with weakly coupled string theory and stays well defined in principle for all other values of its parameters. In other words, we never understood strings well enough to even know what it would mean for the duality to "break down". It is conceivable that somebody might find another way of doing non-perturbative string theory which disagrees with Super Yang-Mills despite passing the same checks but so far that hasn't happened.

Connor Behan
  • 10,659