One-loop effective action of the holographic antisymmetric Wilson loop

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 ${\mathrm{AdS}}_5\times S^5$ 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 ${\mathrm{AdS}}_2\times S^4$ world volume 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.