Identification of the infrared counterpart of SGR 1935+2154 with the Hubble Space Telescope.

We present deep Hubble Space Telescope observations of a new magnetar source, the soft gamma-repeater SGR 1935+2154, discovered by Swift. We obtained three epochs of observations: while the source was active in March 2015, during a quiescent period in August 2015, and during a further active phase in May 2016. Close to the center of the X-ray error region identified by Chandra we find a faint (F140W(AB)=25.3) source, which fades by a factor of ~2 over the course of 5 months between the first two epochs of observations, before rebrightening during the second active period. If this source is indeed the counterpart to SGR 1935+2154 then it is amongst the faintest yet located for a magnetar. Our observations are spaced over 1.3 years and enable us to place limits on the source velocity of $\mu = (60 \pm 40)$ km s$^{-1}$ kpc$^{-1}$; observations on timescales of a decade can hence probe proper motion limits smaller than the velocities observed for the majority of pulsars. The comparison of the optical/IR and X-ray lightcurves of the source suggests that emission in the two regimes is associated but not directly correlated, offering support for a magnetospheric versus a fallback disc origin.