The AdS/QCD Correspondence: Still Undelivered

Abstract

We consider the particle spectrum and event shapes in large N gauge theories in different regimes of the short-distance 't Hooft coupling, lambda. The mesons in the small lambda limit should have a Regge spectrum in order to agree with perturbation theory, while generically the large lambda theories with gravity duals produce spectra reminiscent of KK modes. We argue that these KK-like states are qualitatively different from QCD modes: they are deeply bound states which are sensitive to short distance interactions rather than the flux tube-like states expected in asymptotically free, confining gauge theories. In addition, we also find that the characteristic event shapes for the large lambda theories with gravity duals are close to spherical, very different from QCD-like (small lambda, small N) and Nambu-Goto-like (small lambda, large N) theories which have jets. This observation is in agreement with the conjecture of Strassler on event shapes in large 't Hooft coupling theories, which was recently proved by Hofman and Maldacena for the conformal case. This conclusion does not change even when considering soft-wall backgrounds in the gravity dual. The picture that emerges is the following: theories with small and large lambda are qualitatively different, while theories with small and large N are qualitatively similar. Thus it seems that it is the relative smallness of the 't Hooft coupling in QCD that prevents a reliable AdS/QCD correspondence from emerging, and that reproducing characteristic QCD-like behavior will require genuine stringy dynamics to be incorporated into any putative dual theory.