  We consider certain 1/4 BPS Wilson loop operators in SU(N) ${\cal N}=4$
supersymmetric Yang-Mills theory, whose expectation value can be computed
exactly via supersymmetric localization. Holographically, these operators are
mapped to fundamental strings in AdS5 x S5. The string on-shell action
reproduces the large N and large coupling limit of the gauge theory expectation
value and, according to the AdS/CFT correspondence, there should also be a
precise match between subleading corrections to these limits. We perform a test
of such match at next-to-leading order in string theory, by deriving the
spectrum of quantum fluctuations around the classical string solution and by
computing the corresponding 1-loop effective action. We discuss in detail the
supermultiplet structure of the fluctuations. To remove a possible source of
ambiguity in the ghost zero mode measure, we compare the 1/4 BPS configuration
with the 1/2 BPS one, dual to a circular Wilson loop. We find a discrepancy
between the string theory result and the gauge theory prediction, confirming a
previous result in the literature. We are able to track the modes from which
this discrepancy originates, as well as the modes that by themselves would give
the expected result.
