Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Short Strings in Three-Dimensional Anti-de Sitter Space: from Weak to Strong Coupling

Simon Ekhammar, Nikolay Gromov, Bogdan Stefański, Charles Thull

TL;DR

This work delivers the first nonperturbative spectral results for strings on AdS$_3\times$S$^3\times$T$^4$ with RR flux by solving the conjectured AdS$_3$ QSC across the full coupling range. It demonstrates a seamless connection between a weak-coupling, spin-chain description and a strong-coupling, string-theoretic regime, where energies organize into flat-space Regge trajectories with KK-induced splittings; the leading strong-coupling scaling is $oldsymbol{\Delta}\sim 2\sqrt{\delta}\,\lambda_h^{1/4}$ with $E_0=0$ and a nonvanishing $E_2$, while subleading weak-coupling corrections arise from a nearest-neighbour $\mathfrak{sl}_2$ spin-chain with wrapping at $\mathcal{O}(h^3)$. The authors develop a convergence-accelerated numerical approach based on polylogarithmic bases to extract precise $\Delta(h)$, validate the results against classical folded-string predictions, and compare with AdS$_3$ Virasoro–Shapiro amplitudes. These results provide concrete spectral data across moduli space, enabling precision holography in AdS$_3$ and offering a platform to test related amplitudes and thermodynamic formulations in RR backgrounds. The work thus offers a quantitative bridge between integrability techniques and stringy dynamics in AdS$_3$ holography, with clear directions for extending to massless modes, mixed flux, and higher-dimensional AdS/CFT settings.

Abstract

We numerically solve the conjectured Quantum Spectral Curve for strings on AdS$_3\times$S$^3\times$T$^4$ with R--R charge from weak to strong coupling. At strong coupling, the spectrum organises into flat-space string mass levels with universal square-root scaling in the string tension at leading order, and additional Kaluza-Klein fine-splitting at subleading order. At weak coupling, the energies are determined by a nearest-neighbour Bethe Ansatz, with universal subleading corrections that are suppressed at large volume.

Short Strings in Three-Dimensional Anti-de Sitter Space: from Weak to Strong Coupling

TL;DR

This work delivers the first nonperturbative spectral results for strings on AdSST with RR flux by solving the conjectured AdS QSC across the full coupling range. It demonstrates a seamless connection between a weak-coupling, spin-chain description and a strong-coupling, string-theoretic regime, where energies organize into flat-space Regge trajectories with KK-induced splittings; the leading strong-coupling scaling is with and a nonvanishing , while subleading weak-coupling corrections arise from a nearest-neighbour spin-chain with wrapping at . The authors develop a convergence-accelerated numerical approach based on polylogarithmic bases to extract precise , validate the results against classical folded-string predictions, and compare with AdS Virasoro–Shapiro amplitudes. These results provide concrete spectral data across moduli space, enabling precision holography in AdS and offering a platform to test related amplitudes and thermodynamic formulations in RR backgrounds. The work thus offers a quantitative bridge between integrability techniques and stringy dynamics in AdS holography, with clear directions for extending to massless modes, mixed flux, and higher-dimensional AdS/CFT settings.

Abstract

We numerically solve the conjectured Quantum Spectral Curve for strings on AdSST with R--R charge from weak to strong coupling. At strong coupling, the spectrum organises into flat-space string mass levels with universal square-root scaling in the string tension at leading order, and additional Kaluza-Klein fine-splitting at subleading order. At weak coupling, the energies are determined by a nearest-neighbour Bethe Ansatz, with universal subleading corrections that are suppressed at large volume.
Paper Structure (16 sections, 34 equations, 1 figure, 2 tables)

This paper contains 16 sections, 34 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. AdS$_3$ and Holography.
  3. Weak Coupling and the CFT Regime.
  4. A Stringy Spectrum.
  5. The AdS$_3$ Quantum Spectral Curve
  6. QSC at weak coupling
  7. Numerical Approach
  8. The numerical algorithm.
  9. The Spectrum At Strong Coupling
  10. Classical String Comparison.
  11. Conclusions and Outlook
  12. acknowledgments
  13. A Brief Reminder of the AdS$_3$ QSC
  14. The analytic solution of the QSC
  15. Comparison with the AdS$_3$ Virasoro-Shapiro Amplitude
  16. ...and 1 more sections

Figures (1)

  • Figure 1: The numerical QSC spectrum for a wide range of couplings, $\lambda_h\equiv 16\pi^2 h^2$, and for different states labelled by their spin, $S$, and R-charge, $J$. A stringy spectrum emerges at strong coupling, with energy levels in agreement with flat-space string theory together with additional KK-modes for the two lowest mass-levels. The gray lines show the strong coupling prediction (\ref{['eq:DeltaStrong']}).