  The nature of the $\gamma$-ray emission from the \emph{Fermi} bubbles is
unknown. Both hadronic and leptonic models have been formulated to explain the
peculiar $\gamma$-ray signal observed by the Fermi-LAT between 0.1-500~GeV. If
this emission continues above $\sim$30~TeV, hadronic models of the \emph{Fermi}
bubbles would provide a significant contribution to the high-energy neutrino
flux detected by the IceCube observatory. Even in models where leptonic
$\gamma$-rays produce the \emph{Fermi} bubbles flux at GeV energies, a hadronic
component may be observable at very high energies. The combination of IceCube
and HAWC measurements have the ability to distinguish these scenarios through a
comparison of the neutrino and $\gamma$-ray fluxes at a similar energy scale.
We examine the most recent four-year dataset produced by the IceCube
collaboration and find no evidence for neutrino emission originating from the
\emph{Fermi} bubbles. In particular, we find that previously suggested excesses
are consistent with the diffuse astrophysical background with a p-value of 0.22
(0.05 in an extreme scenario that all the IceCube events that overlap with the
bubbles come from them). Moreover, we show that existing and upcoming HAWC
observations provide independent constraints on any neutrino emission from the
\emph{Fermi} bubbles, due to the close correlation between the $\gamma$-ray and
neutrino fluxes in hadronic interactions. The combination of these results
disfavors a significant contribution from the \emph{Fermi} bubbles to the
IceCube neutrino flux.

High Energy Astrophysical Phenomena