Carrollian supersymmetry and SYK-like models

This work challenges the conventional notion that in a 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 nonrelativistic and ultrarelativistic sectors, we reveal that an ultrarelativistic (Carrollian) supersymmetric Lagrangian exhibits an exotic feature; that is, it 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 Sachdev-Ye-Kitaev (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.