  Warm dark matter particles with masses in the keV range have been linked with
the large group representations in gauge theories through a high number of
species at decoupling. In this paper, we address WDM fermionic degrees of
freedom from such representations. Bridging higher-dimensional particle physics
theories with cosmology studies and astrophysical observations, our approach is
two-folded, i.e., it includes realistic models from higher-dimensional
representations and constraints from simulations tested against observations.
Starting with superalgebras in exceptional periodicity theories, we discuss
several symmetry reductions and we consider several representations that
accommodate a high number of degrees of freedom. We isolate a model that
naturally accommodates both the standard model representation and the fermionic
dark matter in agreement with both large and small-scale constraints. This
model considers an intersection of branes in $D=27+3$ in a manner that provides
the degrees of freedom for the standard model on one hand and 2048 fermionic
degrees of freedom for dark matter, corresponding to a $\sim$2 keV particle
mass, on the other. In this context, we discuss the theoretical implications
and the observable predictions.
