  We study a $d$-dimensional wave equation model ($2\leq d\leq 4$) with
quadratic non-linearity and stochastic forcing given by a space-time fractional
noise. Two different regimes are exhibited, depending on the Hurst parameter
$H=(H_0,\ldots,H_d) \in (0,1)^{d+1}$ of the noise: if $\sum_{i=0}^d H_i >
d-\frac12$, then the equation can be treated directly, while in the case
$d-\frac34<\sum_{i=0}^d H_i\leq d-\frac12$, the model must be interpreted in
the Wick sense, through a renormalization procedure. Our arguments essentially
rely on a fractional extension of the considerations of
\cite{gubinelli-koch-oh} for the two-dimensional white-noise situation, and
more generally follow a series of investigations related to stochastic wave
models with polynomial perturbation.
