  By wrapping D3-branes over 3-cycles on a half-flat manifold we construct an
effective supersymmetric black hole in the N=2 low-energy theory in
four-dimensions. Specifically we find that the torsion cycles present in a
half-flat compactification, corresponding to the mirror symmetric image of
electric NS flux on a Calabi-Yau manifold, manifest in the half-flat black hole
as quantum hair. We compute the electric and magnetic charges related to the
quantum hair, and also the mass contribution to the effective black hole. We
find that by wrapping a number of D3-branes equal to the order of the discrete
group associated to the torsional part of the half-flat homology, the effective
charge and mass terms vanishes. We compute the variation of entropy and the
corresponding temperature associated with the lost of quantum hair. We also
comment on the equivalence between canceling Freed-Witten anomaly and the
assumption of self-duality for the 5-form field strength. Finally from a
K-theoretical perspective, we compute the presence of discrete RR charge of
D-branes wrapping torsional cycles in a half-flat manifold.
