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A bstract This paper is an extension of our last 1D,    $$ \mathcal{N} $$  N = 4 supersymmetric SYK paper [1]. In this paper we introduced the complex linear supermultiplet (CLS), which is “usefully inequivalent” to the chiral supermultiplet. We construct three types of models based on the complex linear supermultiplet containing quartic interactions from modified CLS kinetic term, quartic interactions from 3-pt vertices integrated over the whole superspace, and 2( q −  1)-pt interactions generated via superpotentials respectively. A strong evidence for the inevitability of dynamical bosons for 1D,    $$ \mathcal{N} $$  N = 4 SYK is also presented.

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