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We revisit the problem of matching the strong coupling expansion of the$\frac{1}{2}$ BPS circular Wilson loops in ${\cal N}=4$ SYM and ABJM gaugetheories with their string theory duals in ${\rm AdS}_5 \times S^5$ and ${\rmAdS}_4 \times CP^3$, at the first subleading (one-loop) order of the expansionaround the minimal surface. We observe that, including the overall factor$1/g_{\rm s}$ of the inverse string coupling constant, as appropriate for theopen string partition function with disk topology, and a universal prefactorproportional to the square root of the string tension $T$, both the SYM andABJM results precisely match the string theory prediction. We provide anexplanation of the origin of the $\sqrt T$ prefactor based on special featuresof the combination of one-loop determinants appearing in the string partitionfunction. The latter also implies a natural generalization $Z_\chi \sim (\sqrtT/g_{\rm s})^\chi$ to higher genus contributions with the Euler number $\chi$,which is consistent with the structure of the $1/N$ corrections found on thegauge theory side.

Strong coupling expansion of circular Wilson loops and string theories in AdS$_5 \times {\rm S}^5$ and AdS$_4 \times {\rm CP}^3$