  We consider the theory of $N$ free Dirac fermions with a uniformly winding
mass, $m e^{iqx}$, in two spacetime dimensions. This theory (which describes
for instance a superconducting current in an $N$-channel wire) has been
proposed to have a higher-spin gravity with scalar matter as the large-$N$
dual. To order $m^2$, however, thermodynamic quantities in it can be computed
using standard general relativity instead. Here, we consider the question if
the same is true for the entanglement entropy (EE). By comparing results
obtained on two sides of the duality, we find that general relativity indeed
accounts correctly for the EE of an interval to order $m^2$ (and all orders in
$q$).
