  We systematically study the spectrum of excitations and the one-loop
determinant of holographic Wilson loop operators in antisymmetric
representations of $\mathcal{N}=4$ supersymmetric Yang-Mills theory.
Holographically, these operators are described by D5-branes carrying electric
flux and wrapping an $S^4 \subset S^5$ in the $AdS_5\times S^5$ bulk
background. We derive the dynamics of both bosonic and fermionic excitations
for such D5-branes. A particularly important configuration in this class is the
D5-brane with $AdS_2\times S^4$ worldvolume and $k$ units of electric flux,
which is dual to the circular Wilson loop in the totally antisymmetric
representation of rank $k$. For this Wilson loop, we obtain the spectrum, show
explicitly that it is supersymmetric and calculate the one-loop effective
action using heat kernel techniques.
