Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Infinite spin limit of semiclassical string states

J. A. Minahan, A. Tirziu, A. A. Tseytlin

TL;DR

The paper analyzes the infinite spin limit of semiclassical strings in AdS5×S5, focusing on regimes where one angular momentum dominates another. It demonstrates that the energy deficit E−J in this limit acquires a universal square-root form and that classical string solutions can be interpreted as bound states of giant magnons. A nontrivial 1-loop check shows exact cancellation between bosonic and fermionic fluctuations, suggesting a remnant worldsheet supersymmetry. The study develops a finite-gap/Bethe-ansatz framework to connect the string and gauge theory descriptions in this limit, showing that the dressing factor decouples and that giant magnons and their bound states arise naturally as finite-gap solutions. The results extend to the SL(2) sector and pulsating/circular strings, reinforcing the robustness of the infinite-spin regime as a tractable window into the string/gauge spectrum.

Abstract

Motivated by recent works of Hofman and Maldacena and Dorey we consider a special infinite spin limit of semiclassical spinning string states in AdS5 x S5. We discuss examples of known folded and circular 2-spin string solutions and demonstrate explicitly that the 1-loop superstring correction to the classical expression for the energy vanishes in the limit when one of the spins is much larger that the other. We also give a general discussion of this limit at the level of integral equations describing finite gap solutions of the string sigma model and argue that the corresponding asymptotic form of the string and gauge Bethe equations is the same.

Infinite spin limit of semiclassical string states

TL;DR

The paper analyzes the infinite spin limit of semiclassical strings in AdS5×S5, focusing on regimes where one angular momentum dominates another. It demonstrates that the energy deficit E−J in this limit acquires a universal square-root form and that classical string solutions can be interpreted as bound states of giant magnons. A nontrivial 1-loop check shows exact cancellation between bosonic and fermionic fluctuations, suggesting a remnant worldsheet supersymmetry. The study develops a finite-gap/Bethe-ansatz framework to connect the string and gauge theory descriptions in this limit, showing that the dressing factor decouples and that giant magnons and their bound states arise naturally as finite-gap solutions. The results extend to the SL(2) sector and pulsating/circular strings, reinforcing the robustness of the infinite-spin regime as a tractable window into the string/gauge spectrum.

Abstract

Motivated by recent works of Hofman and Maldacena and Dorey we consider a special infinite spin limit of semiclassical spinning string states in AdS5 x S5. We discuss examples of known folded and circular 2-spin string solutions and demonstrate explicitly that the 1-loop superstring correction to the classical expression for the energy vanishes in the limit when one of the spins is much larger that the other. We also give a general discussion of this limit at the level of integral equations describing finite gap solutions of the string sigma model and argue that the corresponding asymptotic form of the string and gauge Bethe equations is the same.

Paper Structure

This paper contains 18 sections, 183 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Large spin limit of classical string solutions on $R \times S^3$
  3. "Giant magnons" with spin
  4. $J_2 \gg J_1$ limit of the folded string solution
  5. $J_2 \gg J_1$ limit of circular string solution
  6. 1-loop correction to the energy of folded and circular string in the $J_2 \to \infty$ limit
  7. Folded string case
  8. Circular string case
  9. Infinite spin limit and bound magnons in integral Bethe equations
  10. Classical finite gap equations for a string on $R \times S^3$
  11. Infinite $J$ limit and matching to asymptotic spin chain Bethe equations
  12. Giant magnons and their bound states as finite-gap solutions
  13. Finite-gap solutions for large spin limits of circular and pulsating strings
  14. Bosonic fluctuations
  15. Fermionic fluctuations
  16. ...and 3 more sections

Figures (3)

  • Figure 1: $\theta(\sigma)=\arcsin[\sqrt{q}\ {\rm sn}(w_{21} \sigma,q)]$, for $q=0.99999999$, $- \pi \leq \sigma \leq \pi$.
  • Figure 2: Condensates for three different values of $J_1$. As $J_1\to0$, the end points of the contour approach the cut.
  • Figure 3: Condensates for strings made up of two giant magnons. (a) is the limit of the folded string and (b) is a pulsating string. The arrows represent the sign of the density while the dashed line in (b) indicates that the condensate is on the lower sheet.