  Galaxy cluster mergers are natural consequences of the structure formation in
the Universe. Such events involve a large amount of energy ($\sim 10^{63}$ erg)
dissipated during the process. Part of this energy can be channelled in
particle acceleration and magnetic field amplification, enhancing non-thermal
emission of the intra- and inter-cluster environment. Recently, low-frequency
observations have detected a bridge of diffuse synchrotron emission connecting
two merging galaxy clusters, Abell 399 and Abell 401. Such a result provides
clear observational evidence of relativistic particles and magnetic fields
in-between clusters. In this work, we have used LOw Frequency ARray (LOFAR)
observations at 144 MHz to study for the first time the polarized emission in
the A399-A401 bridge region. No polarized emission was detected from the bridge
region. Assuming a model where polarization is generated by multiple shocks,
depolarization can be due to Faraday dispersion in the foreground medium with
respect to the shocks. We constrained its Faraday dispersion to be greater than
0.10 rad m$^{-2}$ at 95% confidence level, which corresponds to an average
magnetic field of the bridge region greater than 0.46 nG (or 0.41 nG if we
include regions of the Faraday spectrum that are contaminated by Galactic
emission). This result is largely consistent with the predictions from
numerical simulations for Mpc regions where the gas density is $\sim 300$ times
larger than the mean gas density.
