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Deeper Look into Short Strings

Nikolay Gromov, Saulius Valatka

TL;DR

This work advances the analytic understanding of short-operator spectra in AdS/CFT by deriving three leading strong-coupling coefficients for small SL(2) operators using Basso's slope conjecture and comparing them with existing Y-system/TBA numerics. It analyzes the folded-string (classical and one-loop) contributions, tests the exact-slope structure, and identifies inconsistencies for higher winding numbers that motivate refinements to the conjectured form. A two-loop strong-coupling prediction is presented, including a concrete case for two magnons, and the results are benchmarked against TBA data via Padé-type fits, showing notable agreement. The study emphasizes the importance of higher-precision numerical data and potential refinements in the slope framework for accurate short-operator predictions at strong coupling. Overall, the work strengthens the bridge between analytic strong-coupling predictions and numerical Y-system/TBA results in the AdS/CFT integrability program.

Abstract

Using a recent conjecture of Basso we compute three leading nontrivial coefficients in the strong coupling expansion of the anomalous dimensions of short operators in the sl2 sector of AdS/CFT. We show that our results are consistent with the numerical results obtained using the Y-system and TBA approach earlier thus providing further support to the Y-system conjecture.

Deeper Look into Short Strings

TL;DR

This work advances the analytic understanding of short-operator spectra in AdS/CFT by deriving three leading strong-coupling coefficients for small SL(2) operators using Basso's slope conjecture and comparing them with existing Y-system/TBA numerics. It analyzes the folded-string (classical and one-loop) contributions, tests the exact-slope structure, and identifies inconsistencies for higher winding numbers that motivate refinements to the conjectured form. A two-loop strong-coupling prediction is presented, including a concrete case for two magnons, and the results are benchmarked against TBA data via Padé-type fits, showing notable agreement. The study emphasizes the importance of higher-precision numerical data and potential refinements in the slope framework for accurate short-operator predictions at strong coupling. Overall, the work strengthens the bridge between analytic strong-coupling predictions and numerical Y-system/TBA results in the AdS/CFT integrability program.

Abstract

Using a recent conjecture of Basso we compute three leading nontrivial coefficients in the strong coupling expansion of the anomalous dimensions of short operators in the sl2 sector of AdS/CFT. We show that our results are consistent with the numerical results obtained using the Y-system and TBA approach earlier thus providing further support to the Y-system conjecture.

Paper Structure

This paper contains 13 sections, 31 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Folded string
  3. Tree level
  4. Discussion of the exact slope and its generalizations
  5. Inconsistencies in the next orders
  6. Two loop prediction
  7. Two loop prediction
  8. TBA numerics
  9. Conclusions
  10. Exact formulae for one-loop correction
  11. Main formula for one-loop correction and notations
  12. One Loop $(S,J)$ Folded String Mathematica Code
  13. $S^3$ and $S^4$ order

Figures (1)

  • Figure 1: Comparison of numeric TBA data to analytic predictions and fits. The plot shows the dependence of the scaling dimension squared of various operators on the coupling $\lambda$ with the leading order contributions subtracted. Solid dots represent numerical data taken from Frolov:2010wt, empty circles for the Konishi state are taken from Gromov:2009zb and empty circles for the $J=3$ state are numerics from Gromov:2011de. $S=2, J=4, n=2$ points are from frolov_private. Solid lines represent fits and the opaque solid lines of corresponding colors show our predictions. Dashed lines stand for $\lambda^{-1/4}$ predictions.