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 N=4 supersymmetric Yang-Mills theory. Holographically, these operators are described by D5-branes carrying electric flux and wrapping an S⁴⊂S⁵ in the AdS₅×S⁵ 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 AdS₂×S⁴ 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.