Abstract
A
bstract
We consider four-derivative superinvariants of five-dimensional
$$ \mathcal{N} $$
N
= 2 supergravity coupled to
n
v
≤ 2 vector multiplets, which we obtain from both the superconformal tensor calculus approach and dimensional reduction. For the minimal case, with no vector multiplets, it is known that there is a unique four-derivative superinvariant. However, for the case of one vector multiplet, after field redefinitions, we find that there are three independent superinvariants, one of which is a vector superinvariant that does not contain any curvatures and takes the form of a supersymmetrization of
F
4
. Similarly, for the two vector multiplet case, corresponding to the STU model, we find three gravitational superinvariants and two
F
4
-type vector superinvariants. Moreover, we find that these vector superinvariants do not affect the two- and three-charge static BPS black hole solutions. We further consider the rigid limit to
$$ \mathcal{N} $$
N
= 2 super-Yang-Mills and use this to conjecture a family of vector superinvariants for five-dimensional
$$ \mathcal{N} $$
N
= 2 supergravity coupled to an arbitrary number of vector multiplets.