New $F^4$ invariants in five-dimensional supergravity

TL;DR

This paper classifies four-derivative superinvariants in five-dimensional $ ext{N}=2$ supergravity with up to two vector multiplets, identifying new invariants and their effects on BPS black holes, and conjectures a general family for arbitrary vector multiplets.

Contribution

It introduces new four-derivative superinvariants in five-dimensional $ ext{N}=2$ supergravity with vector multiplets, extending previous knowledge and providing a conjecture for general cases.

Findings

Identified three independent superinvariants for one vector multiplet.

Found three gravitational and two $F^4$-type vector superinvariants for two vector multiplets.

Superinvariants do not modify two- and three-charge BPS black hole solutions.

Abstract

We consider four-derivative superinvariants of five-dimensional $\mathcal N=2$ supergravity coupled to $n_v\le 2$ 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 $\mathcal N=2$ super-Yang-Mills and use this to conjecture a family of vector superinvariants for five-dimensional $\mathcal N=2$ supergravity coupled to an arbitrary number of vector multiplets.