Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Semiclassical folded string in AdS4 X CP3

Matteo Beccaria, Guido Macorini, CarloAlberto Ratti, Saulius Valatka

TL;DR

This paper develops a complete semiclassical framework for a folded string spinning in $AdS_4\times \mathbb{CP}^3$, providing a compact integral representation for the one-loop energy correction $E_1$ via algebraic-curve methods. It analyzes both short- and long-string regimes, deriving explicit small-spin and large-spin expansions and revealing ABJM-specific wrapping effects that modify the slope function $\sigma(J)$ compared to the $AdS_5\times S^5$ case. The work establishes how the one-loop energy decomposes into anomaly, dressing, and wrapping contributions, and it presents precise weak- and strong-coupling results, including a predictive structure for short states and a detailed discussion of scheme dependence between worldsheet and algebraic-curve regularizations. Overall, the results sharpen the understanding of semiclassical strings in ABJM, with implications for the dual $\,\mathcal{N}=6$ Chern-Simons-matter theory and tests of integrability-based predictions.

Abstract

We consider type IIA superstring theory on the background AdS4 x CP3, and the classical solution describing a folded string spinning in AdS4 with angular momentum in CP3. 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 x S5.

Semiclassical folded string in AdS4 X CP3

TL;DR

This paper develops a complete semiclassical framework for a folded string spinning in , providing a compact integral representation for the one-loop energy correction via algebraic-curve methods. It analyzes both short- and long-string regimes, deriving explicit small-spin and large-spin expansions and revealing ABJM-specific wrapping effects that modify the slope function compared to the case. The work establishes how the one-loop energy decomposes into anomaly, dressing, and wrapping contributions, and it presents precise weak- and strong-coupling results, including a predictive structure for short states and a detailed discussion of scheme dependence between worldsheet and algebraic-curve regularizations. Overall, the results sharpen the understanding of semiclassical strings in ABJM, with implications for the dual Chern-Simons-matter theory and tests of integrability-based predictions.

Abstract

We consider type IIA superstring theory on the background AdS4 x CP3, and the classical solution describing a folded string spinning in AdS4 with angular momentum in CP3. 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 x S5.

Paper Structure

This paper contains 17 sections, 69 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Algebraic curve quantization in $AdS_{4}\times \mathbb{CP}^{3}$
  3. Semiclassical quantization
  4. The folded string in $AdS_{4}\times \mathbb{CP}^{3}$
  5. Quasi-momenta
  6. Integral representation for the one-loop correction to the energy
  7. Short string limit
  8. Fixed $\mathcal{J}$ expansion
  9. Fixed $\rho = \mathcal{J} / \sqrt\mathcal{S}$ expansion
  10. Summation issues
  11. The slope function
  12. Weak coupling
  13. Long string limit
  14. Relation with marginality condition
  15. Prediction for short states
  16. ...and 2 more sections

Figures (1)

  • Figure 1: Asymptotic expansion (\ref{['eq:GV']}) [solid line] and exact numerical $E_{1}$ [dashed line] as functions of $\mathcal{S}$ at $\mathcal{J}=1/5$.