  We construct solutions of a renormalized continuum fractional parabolic
Anderson model, formally given by $\partial_t u=-(-\Delta)^{1/2}u+\xi u$, where
$\xi$ is a periodic spatial white noise. To be precise, we construct limits as
$\varepsilon\to 0$ to solutions of $\partial_t
u_\varepsilon=-(-\Delta)^{1/2}u_\varepsilon+(\xi_\varepsilon-C_\varepsilon)u_\varepsilon$,
where $\xi_\varepsilon$ is a mollification of $\xi$ at scale $\varepsilon$ and
$C_\varepsilon$ is a logarithmically diverging renormalization constant. We use
a simple renormalization scheme based on that of Hairer and Labb\'e, "A simple
construction of the continuum parabolic Anderson model on $\mathbf{R}^{2}$."
