# Vector models and generalized SYK models

## TL;DR

This paper explores the connection between SYK-like models and vector models through a toy model involving tensor and vector fields, revealing phase transitions and symmetry properties relevant to quantum chaos.

## Contribution

It introduces a toy model coupling tensor and vector fields, demonstrating how it reduces to the Gross-Neveu model and flows to an SYK-like model, highlighting phase transitions and symmetry enhancements.

## Key findings

- The toy model reduces to the Gross-Neveu model in 1D.
- A phase transition between chaotic and non-chaotic states occurs based on perturbation sign.
- Models exhibit chaos and enhanced reparameterization symmetries.

## Abstract

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.