  A monochromatic line in the cosmic neutrino spectrum would be a smoking gun
signature of dark matter. It is intriguing that the IceCube experiment has
recently reported two PeV neutrino events with energies that may be equal up to
experimental uncertainties, and which have a probability of being a background
fluctuation estimated to be less than a percent. Here we explore prospects for
these events to be the first indication of a monochromatic line signal from
dark matter. While measurable annihilation signatures would seem to be
impossible at such energies, we discuss the dark matter quantum numbers,
effective operators, and lifetimes which could lead to an appropriate signal
from dark matter decays. We will show that the set of possible decay operators
is rather constrained, and will focus on several viable candidates which could
explain the IceCube events; R-parity violating gravitinos, hidden sector gauge
bosons, and singlet fermions in an extra dimension. In essentially all cases we
find that a PeV neutrino line signal from dark matter would be accompanied by a
potentially observable continuum spectrum of neutrinos rising towards lower
energies.
