  We present a targeted search for blazar flux-correlated high-energy
($\varepsilon_\nu > 1$ TeV) neutrinos from six bright northern blazars, using
the public database of northern-hemisphere neutrinos detected during "IC40"
40-string operations of the IceCube neutrino observatory (April 2008 to May
2009). Our six targeted blazars are subjects of long-term monitoring campaigns
by the VERITAS TeV gamma-ray observatory. We use the publicly-available VERITAS
lightcurves to identify periods of excess and flaring emission. These
predefined intervals serve as our "active temporal windows" in a search for an
excess of neutrinos, relative to Poisson fluctuations of the near-isotropic
atmospheric neutrino background which dominates at these energies. After
defining the parameters of an optimized search, we confirm the expected Poisson
behavior with Monte Carlo simulations prior to testing for excess neutrinos in
the actual data. We make two searches: One for excess neutrinos associated with
the bright flares of Mrk 421 that occurred during the IC40 run, and one for
excess neutrinos associated with the brightest emission periods of five other
blazars (Mrk 501, 1ES 0805+524, 1ES 1218+304, 3C66A, and W Comae), all
significantly fainter than the Mrk 421 flares. We find no significant excess of
neutrinos from the preselected blazar directions during the selected temporal
windows. We derive 90%-confidence upper limits on the number of expected
flux-associated neutrinos from each search. These limits are consistent with
previous point-source searches and Fermi GeV flux-correlated searches. Our
upper limits are sufficiently close to the physically-interesting regime that
we anticipate future analyses using already-collected data will either
constrain models or yield discovery of the first blazar-associated high-energy
neutrinos.
