  We study linear spectral statistics of $N \times N$ Wigner random matrices
$\mathcal{H}$ on mesoscopic scales. Under mild assumptions on the matrix
entries of $\mathcal{H}$, we prove that after centering and normalizing, the
trace of the resolvent $\mathrm{Tr}(\mathcal{H}-z)^{-1}$ converges to a
stationary Gaussian process as $N \to \infty$ on scales $N^{-1/3} \ll
\mathrm{Im}(z) \ll 1$ and explicitly compute the covariance structure. The
limit process is related to certain regularizations of fractional Brownian
motion and logarithmically correlated fields appearing in \cite{FKS13}.
Finally, we extend our results to general mesoscopic linear statistics and
prove that the limiting covariance is given by the $H^{1/2}$-norm of the test
functions.
