A Supersymmetric SYK-like Tensor Model

TL;DR

This paper introduces a supersymmetric tensor model similar to SYK without disorder, demonstrating its large-N behavior and IR solutions that match the supersymmetric SYK model, expanding understanding of tensor models in quantum many-body physics.

Contribution

It constructs a new supersymmetric tensor model without quenched disorder and proves its large-N limit and IR behavior align with the supersymmetric SYK model.

Findings

Large-N limit dominated by melon diagrams

IR solution matches supersymmetric SYK model

Model provides a disorder-free supersymmetric tensor framework

Abstract

We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, "quarks" and "mesons". We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic "melon" diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model.