On 1D, $$ \mathcal{N} $$ = 4 supersymmetric SYK-type models. Part I

Proposals are made to describe 1D, N = 4 supersymmetrical systems that extend SYK models by compactifying from 4D, 1 supersymmetric Lagrangians involving chiral, vector, and tensor supermultiplets. Quartic fermionic vertices generated via integrals over the whole superspace, while 2(q-1)-point superpotentials. The coupling constants in superfield arbitrary, can be chosen Gaussian random. In case, these would exhibit Wishart-Laguerre randomness, which share same feature among other 1D literature. One difference with 2 though, is our contain dynamical bosons, but this consistent 2D, Added conjectures on duality possible mirror symmetry realizations noted.