# Quenched equals annealed at leading order in the colored SYK model

## TL;DR

This paper analyzes a colored SYK model, demonstrating that at leading order, quenched and annealed free energies are identical, and provides a framework for studying $1/N$ corrections systematically.

## Contribution

It introduces a colored version of the SYK model and proves that quenched and annealed free energies coincide at leading order, enabling systematic analysis of $1/N$ corrections.

## Key findings

- Quenched and annealed free energies are identical at leading order.
- Full $1/N$ series for free energies are obtained.
- Framework for systematic $1/N$ correction analysis is developed.

## Abstract

We consider a colored version of the SYK model, that is we distinguish the $D$ vector fermionic fields involved in the interaction by a color. We obtain the full $1/N$ series of both the quenched and annealed free energies of the model and show that at leading order the two are identical. The results can be used to study systematically the $1/N$ corrections to this leading order behavior.