Disordered vector models: from higher spins to incipient strings

Abstract

We present a one-parameter family of large $N$ disordered models, with and without supersymmetry, in three spacetime dimensions. They interpolate from the critical large $N$ vector model dual to a classical higher spin theory, towards a theory with a classical string dual. We analyze the spectrum and OPE data of the theories. While the supersymmetric model is always well-behaved the non-supersymmetric model is unitary only over a small parameter range. We offer some speculations on the origin of strings from the higher spins.

7 pages + appendix, several figures. v2: minor changes, published version