Superactions

We present a general formalism for constructing super-invariants by integrating over even-dimensional submanifolds of superspace, valid for all N. This result includes all previous action formulae, without central changes, and we use it to derive the on-shell N=4 super-Yang-Mills action and a manifestly SU(8) invariant linearized three-loop counterterm for N=8 supergravity. We also present a compact diagrammatic technique that replaces index manipulation involving spinor derivatives.