Title: SYK Models and SYK-like Tensor Models with Global Symmetry,
Abstract: In this paper, we study an SYK model and an SYK-like tensor model with global
symmetry. First, we study the large $N$ expansion of the bi-local collective
action for the SYK model with manifest global symmetry. We show that the global
symmetry is enhanced to a local symmetry at strong coupling limit, and the
corresponding symmetry algebra is the Kac-Moody algebra. The emergent local
symmetry together with the emergent reparametrization is spontaneously and
explicit broken. This leads to a low energy effective action. We evaluate four
point functions, and obtain spectrum of our model. We derive the low energy
effective action and analyze the chaotic behavior of the four point functions.
We also consider the recent 3D gravity conjecture for our model.
We also introduce an SYK-like tensor model with global symmetry. We first
study chaotic behavior of four point functions in various channels for the
rank-3 case, and generalize this into a rank-$(q-1)$ tensor model.