  We studied the leading area term of the entanglement entropy of
$\mathcal{N}=1$ supersymmetric $O(N)$ vector model in $2+1$ dimensions close to
the line of second order phase transition in the large $N$ limit. We found that
the area term is independent of the varying interaction coupling along the
critical line, unlike what is expected in a perturbative theory. Along the way,
we studied non-commuting limits $n-1\to 0$ verses UV cutoff $r\to 0$ when
evaluating the gap equation and found a match only when appropriate counter
term is introduced and whose coupling is chosen to take its fixed point value.
As a bonus, we also studied Fermionic Green's functions in the conical
background. We made the observation of a map between the problem and the
relativistic hydrogen atom.
