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The string theory calculation of the 1/2-BPS circular Wilson loop of N=4 SYMin the planar limit at next to leading order at strong coupling is revisited inthe ratio of its semiclassical string partition function and the one dual to alatitude Wilson loop with trivial expectation value. After applying a conformaltransformation from the disk to the cylinder, this problem can be approached bymeans of the Gel'fand-Yaglom formalism. Using results from the literature andthe exclusion of zero modes from a modified Gel'fand-Yaglom formula, we obtainmatching with the known field theory result. As seen in the phaseshift methodcomputation, non-zero mode contributions cancel and the end result comes fromthe zero mode degeneracies of the latitude Wilson loop.

On precision holography for the circular Wilson loop in $AdS_{5}\times S^{5}$