  The first interactions of photon-induced showers are of electromagnetic
nature, and the transfer of energy to the hadron/muon channel is reduced with
respect to the bulk of hadron-induced showers. This results in a lower number
of secondary muons. Additionally, as the development of photon showers is
delayed by the typically small multiplicity of electromagnetic interactions,
their maximum of shower development is deeper in the atmosphere than for
showers initiated by hadrons. These salient features have enabled searches for
photon showers at the Pierre Auger Observatory. They have led to stringent
upper limits on ultra-high-energy gamma-ray fluxes over four orders in
magnitude in energy. These limits are not only of considerable astrophysical
interest, but they also allow us to constrain beyond-standard-physics
scenarios. For instance, dark matter particles could be superheavy, provided
their lifetime is much longer than the age of the universe. Constraints on
specific extensions of the Standard Model of particle physics that meet the
lifetime requirement for a superheavy particle will be presented. They include
limits on instanton strength as well as on mixing angle between active and
sterile neutrinos.
