  A large fraction of stars is found to be part of binary or higher-order
multiple systems. The ubiquity of planets found around single stars raises the
question if and how planets in binary systems may form. Protoplanetary disks
are the birthplaces of planets, and their characterization is crucial in order
to understand the planet formation process. Our aim is to characterize the
morphology of the GG Tau A disk, one of the largest and most massive
circumbinary disks, and trace evidence for binary-disk interactions. We
obtained observations in polarized scattered light of GG Tau A using the
SPHERE/IRDIS instrument in the H-band filter. We analyze the observed disk
morphology and substructures. We run 2D hydrodynamical models simulating the
evolution of the circumbinary ring over the lifetime of the disk. The disk, as
well as the cavity and the inner region are highly structured with several
shadowed regions, spiral structures, and streamer-like filaments, some of them
detected for the first time. The streamer-like filaments appear to connect the
outer ring with the northern arc. Their azimuthal spacing suggests that they
may be generated by periodic perturbations by the binary, tearing off material
from the inner edge of the outer disk once during each orbit. By comparing
observations to hydrodynamical simulations we find that the main features, in
particular the gap size, as well as the spiral and streamer filaments, can be
qualitatively explained by the gravitational interactions of a binary with
semi-major axis of $\sim$35 au on an orbit coplanar with the circumbinary ring.
