A line of CFTs: from generalized free fields to SYK

Abstract

We point out that there is a simple variant of the SYK model, which we call cSYK, that is SL(2, ℝ) invariant for all values of the coupling. The modification consists of replacing the UV part of the SYK action with a quadratic bilocal term. The corresponding bulk dual is a non-gravitational theory in a rigid AdS2 background. At weak coupling cSYK is a generalized free field theory; at strong coupling, it approaches the infrared of SYK. The existence of this line of fixed points explains the previously found connection between the three-point function of bilinears in these two theories at large q.