  Monochromatic photons could be produced in the annihilation or decay of dark
matter particles. At high energies, the search for such line features in the
cosmic gamma-ray spectrum is essentially background free because plausible
astrophysical processes are not expected to produce such a signal. The
observation of a gamma-ray line would hence be a `smoking-gun' signature for
dark matter, making the search for such signals particularly attractive. Among
the different dark matter models predicting gamma-ray lines, the local
supersymmetric extension of the standard model with small R-parity violation
and gravitino LSP is of particular interest because it provides a framework
where primordial nucleosynthesis, gravitino dark matter and thermal
leptogenesis are naturally consistent. Using the two-years Fermi LAT data, we
present a dedicated search for gamma-ray lines coming from dark matter
annihilation or decay in the Galactic halo. Taking into account the full
detector response, and using a binned profile likelihood method, we search for
significant line features in the energy spectrum of the diffuse flux observed
in different regions of the sky. No evidence for a line signal at the 5-sigma
level is found for photon energies between 1 and 300 GeV, and conservative
bounds on dark matter decay rates and annihilation cross sections are
presented. Implications for gravitino dark matter in presence of small R-parity
violation are discussed, as well as the impact of our results on the prospect
for seeing long-lived neutralinos or staus at the LHC.
