Strong coupling expansion of circular Wilson loops and string theories in AdS5 × S5 and AdS4 × CP3
Simone Giombi, Arkady A. Tseytlin
Abstract
A bstract We revisit the problem of matching the strong coupling expansion of the $$ \frac{1}{2} $$ <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> BPS circular Wilson loops in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> = 4 SYM and ABJM gauge theories with their string theory duals in AdS 5 × S 5 and AdS 4 × CP 3 , at the first subleading (one-loop) order of the expansion around the minimal surface. We observe that, including the overall factor 1/ g s 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 T , both the SYM and ABJM results precisely match the string theory prediction. We provide an explanation of the origin of the $$ \sqrt{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mi>T</mml:mi></mml:msqrt></mml:math> 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 Z χ ∼ ( $$ \sqrt{T}/{g}_{\mathrm{s}} $$ <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> ) χ to higher genus contributions with the Euler number χ , which is consistent with the structure of the 1/ N corrections found on the gauge theory side.