Higher Order Invariants in Supergravity

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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 $\k$-invariant higher order terms, thus re-opening the question of $\k$-invariant ``rigidity'' terms. Finally we describe a recent construction of such an action using the superembedding formalism.
13 pages, Latex. Invited lecture at "Supergravity at 25", Stony Brook, December 2001. V2: Some misprints corrected and a reference added

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