Towards a String Dual of SYK

Abstract

We propose a paradigm for realizing the SYK model within string theory. Using the large $N$ matrix description of $c<1$ string theory, we show that the effective theory on a large number $Q$ of FZZT D-branes in $(p,1)$ minimal string theory takes the form of the disorder averaged SYK model with $J \psi^{p}$ interaction. The SYK fermions represent open strings between the FZZT branes and the ZZ branes that underly the matrix model. The continuum SYK dynamics arises upon taking the large $Q$ limit. We observe several qualitative and quantitative links between the SYK model and $(p,q)$ minimal string theory and propose that the two describe different phases of a single system. We comment on the dual string interpretation of double scaled SYK and on the relevance of our results to the recent discussion of the role of ensemble averaging in holography.