The D-2k R-4 invariants of N=8 supergravity

The existence of a linearized SUSY invariant for N = 8 supergravity whose gravitational components are usually called R4 was established long ago by on-shell superspace arguments. Superspace and string theory methods have also established analogous higher dimensional D2kR4 invariants. However, very little is known about the SUSY completions of these operators which involve other fields of the theory. In this paper we find the detailed component expansion of the linearized R4 invariant starting from the corresponding superamplitude which generates all component matrix elements of the operator. It is then quite straightforward to extend results to the entire set of D2kR4 operators. © SISSA 2011