Higher Order Invariants in Supergravity

On a historical note, we first describe the early superspace construction of counterterms in supergravity and then move on to a brief discussion of selected areas in string theory where higher order supergravity invariants enter the effective theories. Motivated by this description we argue that it is important to understand p-brane actions with κ-invariant higher order terms, thus re-opening the question of κ-invariant “rigidity” terms. Finally we describe a recent construction of such an action using the superembedding formalism. Invited lecture at “Supergravity at 25”, Stony Brook, December 2001. e-mail: [email protected]