Only Flat Spacetime is Full BPS in Four Dimensional N=3 and N=4 Supergravity

TL;DR

This paper proves that in certain N=3 and N=4 supergravity theories, flat spacetime is the only fully supersymmetric solution, contrasting with N=2 theories which admit additional solutions like $AdS_2\times S^2$.

Contribution

It demonstrates that only flat spacetime is fully supersymmetric in specific higher derivative N=3 and N=4 supergravity models, clarifying differences with N=2 theories.

Findings

Flat spacetime is the only fully supersymmetric solution in N=3 and N=4 supergravity.

N=2 supergravity admits additional fully supersymmetric solutions such as $AdS_2\times S^2$.

The paper explains the reason for the richer vacua in N=2 supergravity.

Abstract

We investigate the fully supersymmetric solutions in a class of N=3 and N=4 higher derivative Poincar\'e supergravity theories. These class of theories are obtained within the framework of conformal supergravity using the standard Weyl multiplet and contains a set of terms related to the Weyl square term by supersymmetry. We work in the superconformal formalism and show that flat spacetime is the only fully supersymmetric solution in these theories. However, in N=2 Poincar\'e supergravity theories that falls into the same class, two fully supersymmetric stationary solutions exist: Bertotti-Robinson geometry ($AdS_2\times S^2$) and flat spacetime, which are known in the literature. We discuss the reason behind the richer vacua in N=2 supergravity compared to its N=3 and N=4 cousins.