Higher order curvature terms in Born-Infeld type brane theories

The field equations associated to Born-Infeld type brane theories are studied by using an auxiliary variables method. This approach hinges on the fact that the expressions defining the physical and geometrical quantities describing the worldvolume are varied independently. The general structure of the Born-Infeld type theories for branes contains the square root of a determinant of a combined matrix between the induced metric on the worldvolume swept out by the brane and a symmetric/antisymmetric tensor depending of gauge, matter or extrinsic curvature terms taking place on the worldvolume. The higher order curvature terms appearing in the determinant form come to play as competition with other effective brane models. Additionally, we suggest a Born-Infeld-Einstein type action for branes where the higher order curvature content is provided by the worldvolume Ricci tensor. This action provide an alternative description of the dynamics of braneworld scenarios.