  The presence of $R$-parity violating (RPV) supersymmetric interactions
involving high-energy neutrinos can lead to resonant production of TeV-scale
squarks inside large-volume neutrino detectors. Using the ultra-high energy
neutrino events observed recently at the IceCube, with the fact that for a
given power-law flux of astrophysical neutrinos, there is no statistically
significant deviation in the current data from the Standard Model expectations,
we derive robust upper limits on the RPV couplings as a function of the
resonantly-produced squark mass, independent of the other unknown model
parameters, as long as the squarks decay dominantly to 2-body final states
involving leptons and quarks through the RPV couplings. With more statistics,
we expect these limits to be comparable/complementary to the existing limits
from direct collider searches and other low-energy processes.
