Supersymmetric R2 actions, conformal invariance and the Lorentz Chern-Simons term in 6 and 10 dimensions

We consider the superconformal extension of R2 actions in 6 and 10 dimensions. We show that the fields of the conformal multiplet alone admit a one parameter family of R2 actions of the form φ[R2µνab + α(R2µνab - 4R2µa + R2)]. In d=6 we give the supersymmetric action for α = 0, while for α ≠ 0 we give partial results. We show that for α = 0 and in a conformal gauge the 3-form field Hµν� has a natural torsion interpretation. In d = 10 we find similar results (except the torsion interpretation) up to variations containing the 7-form field strength.