  The Wilson loop operator in the $U(N)_k \times U(N)_{-k}$ ABJM theory at
large $N$ and fixed level $k$ has a dual description in terms of a wrapped M2
brane in the M-theory background AdS$_4 \times S^7/\mathbb Z_k$. We consider
the localization result for the $1\over 2$-BPS circular Wilson loop expectation
value $W$ in this regime, and compare it to the prediction of the M2 brane
theory. The leading large $N$ exponential factor is matched as expected by the
classical action of the M2 brane solution with AdS$_2\times S^1$ geometry. We
show that the subleading $k$-dependent prefactor in $W$ is also exactly
reproduced by the one-loop term in the partition function of the wrapped M2
brane (with all Kaluza-Klein modes included). This appears to be the first case
of an exact matching of the overall numerical prefactor in the Wilson loop
expectation value against the dual holographic result. It provides an example
of a consistent quantum M2 brane computation, suggesting various
generalizations.
