  In the context of $\mathcal{N}=2$ supergravity without vector multiplets
coupled to hypermultiplets, the coupling constant of graviphoton $\tau$ is
apriori a free parameter. Stringy realization of this and using a mathematical
conjecture leads to the statement that $j(\tau)\in \mathbb{R}$ so that the
$\theta$-angle is $0$ or $\pi$. We conjecture that for any consistent
realization of $\mathcal{N}=2$ supergravity theories coupled only to
hypermultiplets this is the case and the rest belong to the swampland. This
leads to the speculation that the $\theta$-angle for QCD or QED may also be
fixed to $0$ for quantum gravitational consistency.
