Four dimensional R^4 superinvariants through gauge completion

TL;DR

This paper computes the complete N=1 supersymmetric R^4 invariants in four-dimensional supergravity, including auxiliary fields and higher-order terms, and explores their implications for quantum supergravity and string theory.

Contribution

It explicitly derives the full supersymmetrization of R^4 terms in N=1 supergravity, including infinite series of terms and their gauge completion in x-space.

Findings

Explicit form of supersymmetric R^4 actions in four dimensions.

Identification of conditions to absorb R^4 terms into supergravity.

Analysis of R^4 terms' relevance to quantum supergravity and string theory.

Abstract

We fully compute the N=1 supersymmetrization of the fourth power of the Weyl tensor in d=4 x-space with the auxiliary fields. In a previous paper, we showed that their elimination requires an infinite number of terms; we explicitely compute those terms to order \kappa^4 (three loop). We also write, in superspace notation, all the possible N=1 actions, in four dimensions, that contain pure R^4 terms (with coupling constants). We explicitely write these actions in terms of the \theta components of the chiral density \epsilon and the supergravity superfields R, G_m, W_{ABC}. Using the method of gauge completion, we compute the necessary \theta components which allow us to write these actions in x-space. We discuss under which circumstances can these extra R^4 correction terms be reabsorbed in the pure supergravity action, and their relevance to the quantum supergravity/string theory effective actions.