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Wrapping interactions at strong coupling -- the giant magnon

Romuald A. Janik, Tomasz Lukowski

TL;DR

The paper develops generalized Luscher-type formulas for finite-size corrections in the nonrelativistic AdS5xS5 worldsheet theory and applies them to compute the giant magnon's finite-J energy shift. By deriving both F- and mu-term corrections for a generic dispersion and incorporating the BES/BHL dressing factor, the authors show that the mu-term, with a Borel-resummed dressing factor, reproduces the classical string result for strong coupling. A thorough analysis across general a-gauges demonstrates the robustness of the approach and the essential influence of the dressing phase. The work provides a stringent, cross-validated framework for finite-size effects beyond the asymptotic Bethe ansatz, with implications for testing integrability-based proposals in AdS/CFT.

Abstract

We derive generalized Luscher formulas for finite size corrections in a theory with a general dispersion relation. For the AdS_5xS^5 superstring these formulas encode leading wrapping interaction effects. We apply the generalized mu-term formula to calculate finite size corrections to the dispersion relation of the giant magnon at strong coupling. The result exactly agrees with the classical string computation of Arutyunov, Frolov and Zamaklar. The agreement involved a Borel resummation of all even loop-orders of the BES/BHL dressing factor thus providing a strong consistency check for the choice of the dressing factor.

Wrapping interactions at strong coupling -- the giant magnon

TL;DR

The paper develops generalized Luscher-type formulas for finite-size corrections in the nonrelativistic AdS5xS5 worldsheet theory and applies them to compute the giant magnon's finite-J energy shift. By deriving both F- and mu-term corrections for a generic dispersion and incorporating the BES/BHL dressing factor, the authors show that the mu-term, with a Borel-resummed dressing factor, reproduces the classical string result for strong coupling. A thorough analysis across general a-gauges demonstrates the robustness of the approach and the essential influence of the dressing phase. The work provides a stringent, cross-validated framework for finite-size effects beyond the asymptotic Bethe ansatz, with implications for testing integrability-based proposals in AdS/CFT.

Abstract

We derive generalized Luscher formulas for finite size corrections in a theory with a general dispersion relation. For the AdS_5xS^5 superstring these formulas encode leading wrapping interaction effects. We apply the generalized mu-term formula to calculate finite size corrections to the dispersion relation of the giant magnon at strong coupling. The result exactly agrees with the classical string computation of Arutyunov, Frolov and Zamaklar. The agreement involved a Borel resummation of all even loop-orders of the BES/BHL dressing factor thus providing a strong consistency check for the choice of the dressing factor.

Paper Structure

This paper contains 10 sections, 134 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Finite size corrections
  3. TBA motivated exponential terms
  4. Diagrammatic derivation of the prefactor
  5. The giant magnon finite $J$ corrections
  6. Conclusions
  7. Evaluation of ${x_q^-}'$
  8. Evaluation of $\sigma^2_{HL}(x_q,x_p)$
  9. Evaluation of $\chi^{(n)}(x,y)$ for $n\geq2$
  10. Borel resummation of $\sigma^2_{n\geq 2}$

Figures (2)

  • Figure 1: The diagram to the left (the $\mu$-term) shows a particle splitting in two virtual, on-shell particles, traveling around the cylinder and recombining. The diagram to the right (the F-term) shows a virtual particle going around the circumference of the cylinder.
  • Figure 2: The graphs giving a leading finite size correction to the self energy: a) $I_{abc}$, b) $J_{abc}$, c) $K_{ab}$. The filled circles are the vertex functions $\Gamma$, empty circles represent the 2-point Green's function. The letter $L$ represents the factor of $e^{-iq^1 L}$ and the letters in italics label the type of particles.