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We compute the 1-loop correction to the effective action for the stringsolution in AdS_5 x S^5 dual to the circular Wilson loop. More generically, themethod we use can be applied whenever the two dimensional spectral problemfactorizes, to regularize and define the fluctuation determinants in terms ofsolutions of one-dimensional differential equations. A such it can be appliedto non-homogeneous solutions both for open and closed strings and to variousboundary conditions. In the case of the circular Wilson loop, we obtain, forthe 1-loop partition function a result which up to a factor of two matches theexpectation from the exact gauge theory computation. The discrepancy can beattributed to an overall constant in the string partition function coming fromthe normalization of zero modes, which we have not fixed.

Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling