  Many aspects of many-body localization (MBL) transitions remain elusive so
far. Here, we propose a higher-dimensional generalization of the
Sachdev-Ye-Kitaev (SYK) model and show that it exhibits a MBL transition. The
model on a bipartite lattice has $N$ Majorana fermions with SYK interactions on
each site of the $A$ sublattice and $M$ free Majorana fermions on each site the
of $B$ sublattice, where $N$ and $M$ are large and finite. For
$r$$\equiv$$M/N\!<\!r_c$=1, it describes a diffusive metal exhibiting maximal
chaos. Remarkably, its diffusive constant $D$ vanishes [$D$$\propto$$
(r_c-r)^{1/2}$] as $r$$\rightarrow$$r_c$, implying a dynamical transition to a
MBL phase. It is further supported by numerical calculations of level
statistics which changes from Wigner-Dyson ($r$$<$$r_c$) to Poisson
($r$$>$$r_c$) distributions. Note that no subdiffusive phase intervenes between
diffusive and MBL phases. Moreover, the critical exponent $\nu$=0, violating
the Harris criterion. Our higher-dimensional SYK model may provide a promising
arena to explore exotic MBL transitions.
