  In this article, we extend our study on a new class of modular Hamiltonians
on an interval attached to the origin on the semi-infinite line, introduced in
a recent work dedicated to scalar fields. Here, we shift our attention to
fermions and similarly to the scalar case, we investigate the modular
Hamiltonians of theories which are obtained through dimensional reduction, this
time, of a free massless Dirac field in $d$ dimensions. By following the same
methodology, we perform dimensional reduction on both the physical and modular
Hamiltonians. This process enables us to establish a correspondence: we
identify the modular Hamiltonian in an interval connected to the origin to the
one obtained from the reduction of the modular Hamiltonian pertaining to the
conformal parent theory on a sphere. Intriguingly, although the resulting
one-dimensional theories lack conformal symmetry due to the presence of a term
proportional to $1/r$, the corresponding modular Hamiltonians are local
functions in the energy density. This phenomenon mirrors the well known
behaviour observed in the conformal case and indicates the existence of a
residual symmetry, characterized by a subset of the original conformal group.
  Furthermore, through an analysis of the spectrum of the modular Hamiltonians,
we derive an analytic expression for the associated entanglement entropy. Our
findings also enable us to successfully recover the conformal anomaly
coefficient from the universal piece of the entropy in even dimensions, as well
as the universal constant $F$ term in $d=3$, by extending the radial
regularization scheme originally introduced by Srednicki to perform the sum
over angular modes.
