Weyl Invariant p - brane and D p - brane actions

Conformal invariant new forms of p-brane and Dp-brane actions are proposed. These are quadratic in ∂X for the p-brane case and for Dp-branes in the Abelian field strength. The fields content of these actions are: an induced metric, gauge fields, an auxiliary metric and an auxiliary scalar field. The proposed actions are Weyl invariant in any dimension and the elimination of the auxiliary metric and the scalar field reproduces the Nambu-Goto action for p-branes and the Born-Infeld action for Dp-branes. Comments on symmetry properties of these actions and the construction of their respective Weyl invariant energy-momentum tensor are worked out. The space-time supersymmetric extension of the p-brane action is constructed. We show explicitly the existence of a Weyl κ-symmetry invariance of the corresponding action. Finally we remark some advantages of these new forms to the canonical analysis and to the inclusion of conformal invariant interactions.