One-loop correction to the energy of spinning strings in S5

We revisit the computation of the 1-loop AdS5xS5 superstring sigma model correction to the energy of a closed circular string rotating in S5. The string is spinning around its center of mass with two equal angular momenta J2=J3 and its center of mass angular momentum is J1. We revise the argument that the 1-loop correction is suppressed by (1/J) factor [J=J1+2J2 is the total SO(6) spin] relative to the classical (λJ2/J2) term in the energy and use numerical methods to compute the leading 1-loop coefficient. The corresponding gauge-theory result is known only in the J1=0 limit when the string solution becomes unstable and thus the 1-loop shift of the energy formally contains an imaginary part. While the comparison with gauge-theory may not be well defined in this case, our numerical string-theory value of the 1-loop coefficient seems to disagree with the gauge-theory one. A plausible explanation should be in the different order of limits taken on the gauge-theory and the string-theory sides of the anti-de Sitter/conformal field theory duality