  Using the harmonic superspace method and the duality between real and complex
representations of hypermultiplets, we compute the explicit scalar field
expression of the quaternionic metric $G_{mn}$ of the moduli space
SO(1,1)x[SO(4,k)/(SO(4)xSO(k))] of 6D N=2 supergravity with generic k Maxwell
supermultiplets. The obtained metric includes the particular case k=20
associated with 10D type IIA superstring on K3. Uplifting to 7D N=2
supergravity is described and aspects of 6D/7D black attractor effective
potentials are studied.
