# Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model

## TL;DR

This paper reveals that the Sachdev-Ye-Kitaev model with Majorana fermions inherently possesses supersymmetry, which is determined by the number of modes and relates to topological phases, impacting correlation functions.

## Contribution

It demonstrates that the SYK model naturally exhibits supersymmetry without specific coupling relations, linking it to topological phases and the Altland-Zirnbauer classification.

## Key findings

- The SYK model is supersymmetric without explicit coupling constraints.
- Supersymmetry is linked to the number of Majorana modes and topological phases.
- Implications for dynamical correlation functions beyond the ground state.

## Abstract

Supersymmetry is a powerful concept in quantum many-body physics. It helps to illuminate ground state properties of complex quantum systems and gives relations between correlation functions. In this work, we show that the Sachdev-Ye-Kitaev model, in its simplest form of Majorana fermions with random four-body interactions, is supersymmetric. In contrast to existing explicitly supersymmetric extensions of the model, the supersymmetry we find requires no relations between couplings. The type of supersymmetry and the structure of the supercharges are entirely set by the number of interacting Majorana modes, and are thus fundamentally linked to the model's Altland-Zirnbauer classification. The supersymmetry we uncover has a natural interpretation in terms of a one-dimensional topological phase supporting Sachdev-Ye-Kitaev boundary physics, and has consequences away from the ground state, including in $q$-body dynamical correlation functions.