Poisson BF theory as the twist of 5d supergravity

Consider 5-dimensional $\mathcal N=1$ supergravity on $\mathbb R^5$. Let $\mathbb C^2$ carry its canonical holomorphic symplectic structure, and let Poisson BF theory be defined on $\mathbb C^2 \times \mathbb R$. 5d supergravity twist conjecture. The twist of 5-dimensional $\mathcal N=1$ supergravity on $\mathbb R^5$ is equivalent to Poisson BF theory on $\mathbb C^2 \times \mathbb R$. This conjectural equivalence connects the Poisson BF theory constructed in the paper with twisted supergravity and motivates the later comparison with twisted super Yang–Mills theory.