  We consider the relation between SYK-like models and vector models by
studying a toy model where a tensor field is coupled with a vector field. By
integrating out the tensor field, the toy model reduces to the Gross-Neveu
model in 1 dimension. On the other hand, a certain perturbation can be turned
on and the toy model flows to an SYK-like model at low energy. A
chaotic-nonchaotic phase transition occurs as the sign of the perturbation is
altered. We further study similar models that possess chaos and enhanced
reparameterization symmetries.
