Semiclassical folded string in AdS5 × S5

We consider type IIA superstring theory on the background \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ Ad{S_4} \times \mathbb{C}{\mathbb{P}^3} $\end{document}, and the classical solution describing a folded string spinning in AdS4 with angular momentum in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathbb{C}{\mathbb{P}^3} $\end{document}. In the ’t Hooft limit, it is the gravity dual of twist operators in the ABJM superconformal theory. We quantize the classical solution by algebraic curve methods and determine the first semiclassical correction to the energy. We provide an integral representation for this quantity valid for all values of the charges. We analyze its properties in the special regimes associated with a short or long string providing various accurate analytical expansions. Finally, we investigate various properties of the so-called slope, the leading term of the energy for short strings, collecting information that could be useful in attempts to generalize the exact results recently proposed for the folded string in AdS5 × S5.