Carrollian Supersymmetry and SYK-like models

TL;DR

This paper reveals that ultra-relativistic (Carrollian) supersymmetric models can exist without purely bosonic terms, linking higher-dimensional Carrollian theories to (0+1)-dimensional SYK-like models, with potential implications for non-AdS holography.

Contribution

It demonstrates the existence of Carrollian supersymmetric Lagrangians lacking purely bosonic parts and connects higher-dimensional theories to SYK-like models.

Findings

Carrollian supersymmetry can be purely fermionic.

Higher-dimensional Carrollian models relate to (0+1)-dimensional SYK models.

Potential applications in non-AdS holography.

Abstract

This work challenges the conventional notion that in spacetime dimension higher than one, a supersymmetric Lagrangian invariably consists of purely bosonic terms, purely fermionic terms, as well as boson-fermion mixing terms. By recasting a relativistic Lagrangian in terms of its non-relativistic and ultra-relativistic sectors, we reveal that an ultra-relativistic (Carrollian) supersymmetric Lagrangian can exist without a purely bosonic contribution. Based on this result, we demonstrate a link between higher-dimensional Carrollian and (0+1)-dimensional quantum mechanical models, yielding higher-order extensions of supersymmetric SYK models in which purely bosonic higher order terms are absent. Given that supersymmetry plays an essential role in improving the quantum behavior and solubility, our findings may lead to interesting applications in non-AdS holography.