Strong coupling expansion of circular Wilson loops and string theories in AdS5 × S5 and AdS4 × CP3

Abstract

<jats:title>A<jats:sc>bstract</jats:sc></jats:title><jats:p>We revisit the problem of matching the strong coupling expansion of the<jats:inline-formula><jats:alternatives><jats:tex-math>$$ \frac{1}{2} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math></jats:alternatives></jats:inline-formula>BPS circular Wilson loops in<jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math></jats:alternatives></jats:inline-formula>= 4 SYM and ABJM gauge theories with their string theory duals in AdS<jats:sub>5</jats:sub><jats:italic>× S</jats:italic><jats:sup>5</jats:sup>and AdS<jats:sub>4</jats:sub><jats:italic>× CP</jats:italic><jats:sup>3</jats:sup>, at the first subleading (one-loop) order of the expansion around the minimal surface. We observe that, including the overall factor 1/<jats:italic>g</jats:italic><jats:sub>s</jats:sub>of the inverse string coupling constant, as appropriate for the open string partition function with disk topology, and a universal prefactor proportional to the square root of the string tension<jats:italic>T</jats:italic>, both the SYM and ABJM results precisely match the string theory prediction. We provide an explanation of the origin of the<jats:inline-formula><jats:alternatives><jats:tex-math>$$ \sqrt{T} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mi>T</mml:mi></mml:msqrt></mml:math></jats:alternatives></jats:inline-formula>prefactor based on special features of the combination of one-loop determinants appearing in the string partition function. The latter also implies a natural generalization<jats:italic>Z</jats:italic><jats:sub><jats:italic>χ</jats:italic></jats:sub>∼ (<jats:inline-formula><jats:alternatives><jats:tex-math>$$ \sqrt{T}/{g}_{\mathrm{s}} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mi>T</mml:mi></mml:msqrt><mml:mo>/</mml:mo><mml:msub><mml:mi>g</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math></jats:alternatives></jats:inline-formula>)<jats:sup><jats:italic>χ</jats:italic></jats:sup>to higher genus contributions with the Euler number<jats:italic>χ</jats:italic>, which is consistent with the structure of the 1/<jats:italic>N</jats:italic>corrections found on the gauge theory side.</jats:p>