Long range SYK model and boundary SYK model

We study a class of long-range solvable models in IR limit which corresponds to a one-dimensional long-range conformal manifold. This class of long-range model can be interpreted as the non-unitary interpolation between the Sachdev-Ye-Kiteav-like model and the free theory. We investigate the chaos and information scrambling of the model by analyzing its out-of-time order correlators. We find the suppression of the Lyapunov exponent by the long-range interaction and a slowdown in butterfly velocity in the emergent light cone which can be interpreted as the contribution from the anomalous dimension of the stress tensor in the spectrum. We further study a Yukawa-SYK model located in a 3-dimensional boundary with a free field living in a 4-dimensional bulk. The boundary IR spectrum of the model contains a tower of the spinning operators protected by the higher spin symmetry of the bulk. We evaluate the central charge and the Lyapunov exponent of the model.