One-loop correction to the energy of spinning strings inS5

Abstract

We revisit the computation of the 1-loop ${\mathrm{A}\mathrm{d}\mathrm{S}}_5\times S^5$ superstring sigma model correction to the energy of a closed circular string rotating in $S^5$. The string is spinning around its center of mass with two equal angular momenta $J_2=J_3$ and its center of mass angular momentum is $J_1$. We revise the argument that the 1-loop correction is suppressed by $\frac{1}{J}$ factor [$J=J_1+2J_2$ is the total SO(6) spin] relative to the classical $\frac{\lambda J_2}{J^2}$ 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 $J_1=0$ 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.