  We develop here a theory of the electronic properties of a finite number of
valence holes in gated WSe$_2$ quantum dots, considering the influence of spin,
valley, electronic orbitals, and many-body interactions. The single-particle
wave functions are constructed by combining the spin-up and down states of the
highest valence bulk bands employing a multi-million atom ab-initio based
tight-binding model solved in the wave-vector space, allowing to study up to
100 nm radius quantum dots atomistically. The effects of the many-body
interactions are determined using the configuration interaction (CI) technique,
applied up to $N = 6$ holes occupying up to 6 electronic shells with 42
orbitals. Our results show that N=2 holes are in valley and spin
anti-ferromagnetic ground state, independent of the interaction strength and
the quantum dot size. However, we predict that higher number of holes can
undergo a transition to spontaneously broken symmetry valley and spin polarized
ferromagnetic phases, highlighting the interplay between the many-body effects
and the quantum dot lateral size and confining potential depth.
