Scaling limits of complex Sachdev-Ye-Kitaev models and holographic geometry

A bstract We compare different limits of the Sachdev-Ye-Kitaev model of N complex fermion with p -fermion interactions. First, we compute the fermion Green’s function and free energy in the limit of large N followed subsequently by the limit of large p . Next, we examine the ‘double-scaling’ limit in which the large N , p limits are taken at fixed λ = p 2 / N . Earlier results on the latter limit are resummed for small λ , and shown to match our results for the first limit. We also describe the holographic match of our results to two-dimensional Jackiw-Teitelboim gravity with an additional U(1) gauge field.