Computing the Scalar Field Couplings in 6D Supergravity

Using non chiral supersymmetry in 6D space time, we compute the explicit expression of the metric the scalar manifold $SO(1,1) \times \frac{SO(4,20) }{SO(4) \times SO(20)}$ of the 10D type IIA superstring on generic K3. We consider as well the scalar field self-couplings in the general case where the non chiral 6D supergravity multiplet is coupled to generic n vector supermultiplets with moduli space $SO(1,1) \times \frac{SO(4,n)}{SO(4) \times SO(n)}$. We also work out a dictionary giving a correspondence between hyperKahler geometry and the Kahler geometry of the Coulomb branch of 10D type IIA on Calabi-Yau threefolds. Others features are also discussed.