The D^{2k} R^4 Invariants of N=8 Supergravity

TL;DR

This paper derives the detailed component expansion of the linearized R^4 invariant in N=8 supergravity, providing insights into the supersymmetric completions of higher-dimensional D^{2k} R^4 operators using superamplitudes.

Contribution

It presents the first explicit component expansion of the linearized R^4 invariant in N=8 supergravity from superamplitudes, extending to D^{2k} R^4 operators.

Findings

Explicit component expansion of R^4 invariant derived

Method to extend results to D^{2k} R^4 operators established

Provides a foundation for understanding SUSY completions of higher operators

Abstract

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