2D supergravity in p+1 dimensions

We describe new N-extended 2D supergravities on a (p + 1)-dimensional (boso nic) space. The fundamental objects are moving frame densities that equip e ach (p + 1)-dimensional point with a 2D "tangent space". The theory is pres ented in a [p + 1,2] superspace. For the special case of p = 1 we recover t he 2D supergravities in an unusual form. The formalism has been developed w ith applications to the string-parton picture of D-branes at strong couplin g in mind. (C) 1999 Elsevier Science B.V.