# SYK Model with global symmetries in the double scaling limit

## TL;DR

This paper extends the SYK model to include global symmetries in the double scaling limit, developing new computational techniques for moments and correlation functions with chemical potentials.

## Contribution

It introduces chord diagram methods and a transfer matrix approach to analyze SYK models with classical group symmetries and fixed charge partition functions.

## Key findings

- Derived explicit formulas for moments and two-point functions with chemical potential.
- Developed a transfer matrix formalism for chord diagram contributions.
- Computed partition functions at fixed charges for orthogonal, unitary, and symplectic groups.

## Abstract

We discuss the double scaling limit of the SYK model with global symmetries. We develop the chord diagram techniques to compute the moments of the Hamiltonian and the two point function in the presence of arbitrary chemical potential. We also derive a transfer matrix acting on an auxiliary Hilbert space which can capture the chord diagram contributions. We present explicit results for the case of classical group symmetries namely orthogonal, unitary and symplectic groups. We also find the partition functions at fixed charges.