  We focus our attention on the one dimensional scalar theories that result
from dimensionally reducing the free scalar field theory in arbitrary d
dimensions. As is well known, after integrating out the angular coordinates,
the free scalar theory can be expressed as an infinite sum of theories living
in the semi-infinite line, labeled by the angular modes $\{l, \vec{m}\}$. We
show that their modular Hamiltonian in an interval attached to the origin is,
in turn, the one obtained from the dimensional reduction of the modular
Hamiltonian of the conformal parent theory in a sphere. Remarkably, this is a
local expression in the energy density, as happens in the conformal case,
although the resulting one dimensional theories are clearly not conformal. We
support this result by analyzing the symmetries of these theories, which turn
out to be a portion of the original conformal group, and proving that the
reduced modular Hamiltonian is in fact the operator generating the modular flow
in the interval. By studying the spectrum of these modular Hamiltonians, we
also provide an analytic expression for the associated entanglement entropy.
Finally, extending the radial regularization scheme originally introduced by
Srednicki, we sum over the angular modes to successfully recover the conformal
anomaly in the entropy logarithmic coefficient in even dimensions, as well as
the universal constant $F$ term in $d = 3$.
