Strong coupling expansion of 1 2 BPS Wilson loop in SYM theory and 2-loop Green-Schwarz string in AdS5 × S5

The exact localization result for the expectation value of the 12 BPS circular Wilson loop in N=4 SYM theory is given in the planar limit by the famous Bessel function expression: 〈W〉=2NλI1(λ). Expanded in large λ and expressed in terms of the AdS5 × S5 string tension T=λ2π this gives 〈W〉=T2πgse2πT(1−316πT−1+…).The exponential is matched by the value of the action of the string with the AdS2 world volume while the prefactor comes from the 1-loop GS string correction. Here we address the question of how the subleading T−1 term could be reproduced by the 2-loop correction in the corresponding partition function of the AdS5 × S5 GS string expanded near the AdS2 minimal surface. We find that the string correction contains a non-zero UV logarithmic divergence implying that comparison with the SYM result requires a particular subtraction prescription. We discuss implications of this conclusion for checking the AdS/CFT duality at strong coupling.