  A polarizable variation of Hodge structure over a smooth complex quasi
projective variety $S$ is said to be defined over a number field $L$ if $S$ and
the algebraic connection associated to the variation are both defined over $L$.
Conjecturally any special subvariety (also called "an irreducible component of
the Hodge locus) for such variations is defined over $\overline{\mathbb{Q}}$,
and its Galois conjugates are also special subvarieties. We prove this
conjecture for special subvarieties satisfying a simple monodromy condition. As
a corollary we reduce the conjecture that special subvarieties for variation of
Hodge structures defined over a number field are defined over
$\overline{\mathbb{Q}}$ to the case of special points.
