Four dimensional "old minimal" N=2 supersymmetrization of R^4

TL;DR

This paper constructs a four-dimensional N=2 supergravity Lagrangian with R^4 terms in superspace, analyzes auxiliary fields, and discusses their eliminability, providing insights into higher-derivative supergravity theories.

Contribution

It presents the first superspace formulation of R^4 terms in N=2 supergravity without local SO(2) symmetry and analyzes auxiliary field dynamics.

Findings

Auxiliary fields in Weyl and vector multiplets have derivatives and cannot be eliminated on-shell.

Auxiliary fields in the nonlinear multiplet do not have derivatives and can be eliminated.

Leading terms of the Lagrangian allow for auxiliary field elimination.

Abstract

We write in superspace the lagrangian containing the fourth power of the Weyl tensor in the "old minimal" d=4, N=2 supergravity, without local SO(2) symmetry. Using gauge completion, we analyze the lagrangian in components. We find out that the auxiliary fields which belong to the Weyl and compensating vector multiplets have derivative terms and therefore cannot be eliminated on-shell. Only the auxiliary fields which belong to the compensating nonlinear multiplet do not get derivatives and could still be eliminated; we check that this is possible in the leading terms of the lagrangian. We compare this result to the similar one of "old minimal" N=1 supergravity and we comment on possible generalizations to other versions of N=1,2 supergravity.