We present results of long-term multi-wavelength polarization observations ofthe powerful blazar 3C~279 after its $\gamma$-ray flare on 2013~December 20. Wefollowed up this flare with single-dish polarization observations using two21-m telescopes of the Korean VLBI Network. Observations carried out weeklyfrom 2013~December~25 to 2015~January~11, at 22~GHz, 43~GHz, 86~GHzsimultaneously, as part of the Monitoring Of GAmma-ray Bright AGN (MOGABA)program. We measured 3C~279 total flux densities of 22--34~Jy at 22~GHz,15--28~Jy (43~GHz), and 10--21~Jy (86~GHz), showing mild variability of $\leq50\,\%$ over the period of our observations. The spectral index between 22~GHzand 86~GHz ranged from $-0.13$ to $-0.36$. Linear polarization angles were27$^{\circ}$--38$^{\circ}$, 30$^{\circ}$--42$^{\circ}$, and33$^{\circ}$--50$^{\circ}$ at 22~GHz, 43~GHz, and 86~GHz, respectively. Thedegree of linear polarization was in the range of 6--12\,\%, and slightlydecreased with time at all frequencies. We investigated Faraday rotation anddepolarization of the polarized emission at 22--86~GHz, and found Faradayrotation measures (RM) of $-300$ to $-1200$~rad~m$^{-2}$ between 22~GHz and43~GHz, and $-800$ to $-5100$~rad~m$^{-2}$ between 43~GHz and 86~GHz. The RMvalues follow a power law with a mean power law index $a$ of $2.2$, implyingthat the polarized emission at these frequencies travels through a Faradayscreen in or near the jet. We conclude that the regions emitting polarizedradio emission may be different from the region responsible for the 2013December $\gamma$-ray flare and are maintained by the dominant magnetic fieldperpendicular to the direction of the radio jet at milliarcsecond scales.
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