  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.
