The D[subscript 2k] R[subscript 4] invariants of N=8 supergravity

Abstract

The existence of a linearized SUSY invariant for N=8 supergravity whose gravitational components are usually called R[superscript 4] was established long ago by on-shell super-space arguments. Superspace and string theory methods have also established analogous higher dimensional D[superscript 2k] R[superscript 4] 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 R[superscript 4] 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 D[superscript 2k] R[superscript 4] operators.