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Precision Spectroscopy of AdS/CFT

N. Beisert, S. Frolov, M. Staudacher, A. A. Tseytlin

TL;DR

The paper investigates precision spectroscopy in AdS5×S5 by comparing semiclassical string energies in the large-charge regime with one-loop anomalous dimensions in planar N=4 SYM, leveraging integrable spin chains and Bethe ansatz techniques. It demonstrates a full analytic match between leading-order string corrections ε1 and gauge-theory δ1 for two-spin states on S^5, and shows that the (S,J) sector is connected to the (J1,J2) sector via analytic continuation with consistent leading-order results. The authors extend the analysis to higher loops, presenting numerical evidence that two-loop results agree within about 1% in the thermodynamic limit, while three-loop results remain inconclusive due to finite-size effects and vertex ambiguities. Overall, the work strengthens the evidence for AdS/CFT in non-BPS sectors and underscores integrability as a powerful tool for dynamical tests and future all-orders developments.

Abstract

We extend recent remarkable progress in the comparison of the dynamical energy spectrum of rotating closed strings in AdS_5xS^5 and the scaling weights of the corresponding non-near-BPS operators in planar N=4 supersymmetric gauge theory. On the string side the computations are feasible, using semiclassical methods, if angular momentum quantum numbers are large. This results in a prediction of gauge theory anomalous dimensions to all orders in the `t Hooft coupling lambda. On the gauge side the direct computation of these dimensions is feasible, using a recently discovered relation to integrable (super) spin chains, provided one considers the lowest order in lambda. This one-loop computation then predicts the small-tension limit of the string spectrum for all (i.e. small or large) quantum numbers. In the overlapping window of large quantum numbers and small effective string tension, the string theory and gauge theory results are found to match in a mathematically highly non-trivial fashion. In particular, we compare energies of states with (i) two large angular momenta in S^5, and (ii) one large angular momentum in AdS_5 and S^5 each, and show that the solutions are related by an analytic continuation. Finally, numerical evidence is presented on the gauge side that the agreement persists also at higher (two) loop order.

Precision Spectroscopy of AdS/CFT

TL;DR

The paper investigates precision spectroscopy in AdS5×S5 by comparing semiclassical string energies in the large-charge regime with one-loop anomalous dimensions in planar N=4 SYM, leveraging integrable spin chains and Bethe ansatz techniques. It demonstrates a full analytic match between leading-order string corrections ε1 and gauge-theory δ1 for two-spin states on S^5, and shows that the (S,J) sector is connected to the (J1,J2) sector via analytic continuation with consistent leading-order results. The authors extend the analysis to higher loops, presenting numerical evidence that two-loop results agree within about 1% in the thermodynamic limit, while three-loop results remain inconclusive due to finite-size effects and vertex ambiguities. Overall, the work strengthens the evidence for AdS/CFT in non-BPS sectors and underscores integrability as a powerful tool for dynamical tests and future all-orders developments.

Abstract

We extend recent remarkable progress in the comparison of the dynamical energy spectrum of rotating closed strings in AdS_5xS^5 and the scaling weights of the corresponding non-near-BPS operators in planar N=4 supersymmetric gauge theory. On the string side the computations are feasible, using semiclassical methods, if angular momentum quantum numbers are large. This results in a prediction of gauge theory anomalous dimensions to all orders in the `t Hooft coupling lambda. On the gauge side the direct computation of these dimensions is feasible, using a recently discovered relation to integrable (super) spin chains, provided one considers the lowest order in lambda. This one-loop computation then predicts the small-tension limit of the string spectrum for all (i.e. small or large) quantum numbers. In the overlapping window of large quantum numbers and small effective string tension, the string theory and gauge theory results are found to match in a mathematically highly non-trivial fashion. In particular, we compare energies of states with (i) two large angular momenta in S^5, and (ii) one large angular momentum in AdS_5 and S^5 each, and show that the solutions are related by an analytic continuation. Finally, numerical evidence is presented on the gauge side that the agreement persists also at higher (two) loop order.

Paper Structure

This paper contains 10 sections, 89 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Strings rotating on $S^5$
  3. Strings rotating on $AdS_5$ and $S^5$
  4. Higher loop corrections
  5. Conclusions and Outlook
  6. Rotating string solutions
  7. Relation between two-spin solutions
  8. Gauge theory details
  9. The circular vs. imaginary solution
  10. Energy as a function of the spins

Figures (1)

  • Figure 1: The leading order correction to the energy $\epsilon_1$ for the folded string solution. The region $J_2/J>0$ correspond to the $(J_1,J_2)$ case, whereas $J_2/J<0$ correspond to the $(S,J)$ case with $S/J=-J_2/J$ and energy $\tilde{\epsilon}_1=-\epsilon_1$. We also plot a mirror image under the symmetry $J_1\leftrightarrow J_2$ (dashed) and the energy of the circular string $\hat{\epsilon}_1$ (dotted).