Semiclassical energy of the $AdS_4 \times \mathbb{CP}^3$ folded string

TL;DR

This paper calculates the first semiclassical correction to the energy of a folded spinning string in $AdS_4 imes ext{CP}^3$, providing a general integral formula and analyzing short and long string regimes.

Contribution

It introduces a novel algebraic curve method to quantize the classical string solution and derive a universal integral representation for the energy correction.

Findings

Derived the first semiclassical energy correction for the folded string.

Provided an integral formula valid for all charge values.

Analyzed energy behavior in short and long string limits.

Abstract

We consider the classical solution describing a folded type IIA string in the background $AdS_4 \times \mathbb{CP}^3$. The string is spinning in $AdS$ and has angular momentum in $\mathbb{CP}^3$. In the 't Hooft limit, this 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. An integral representation is given, valid for all values of the charges. We analyze its properties in the special regimes associated with a short or long string. Finally, we investigate various properties of the leading term of the energy for short strings (the so-called slope).