# A line of CFTs: from generalized free fields to SYK

## TL;DR

This paper introduces cSYK, a variant of the SYK model with $SL(2,R)$ invariance at all couplings, connecting generalized free fields to SYK and revealing a continuous line of fixed points.

## Contribution

It presents a simple modification of the SYK model, called cSYK, that maintains $SL(2,R)$ invariance across all couplings and links generalized free fields to SYK in a unified framework.

## Key findings

- cSYK is $SL(2,R)$ invariant for all couplings.
- At weak coupling, cSYK behaves as a generalized free field.
- At strong coupling, cSYK approaches the infrared of SYK.

## Abstract

We point out that there is a simple variant of the SYK model, which we call cSYK, that is $SL(2,R)$ invariant for all values of the coupling. The modification consists of replacing the UV part of the SYK action with a quadratic bilocal term. The corresponding bulk dual is a non-gravitational theory in a rigid AdS$_2$ background. At weak coupling cSYK is a generalized free field theory; at strong coupling, it approaches the infrared of SYK. The existence of this line of fixed points explains the previously found connection between the three-point function of bilinears in these two theories at large $q$.