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Giant magnons in AdS_4/CFT_3: dispersion, quantization and finite--size corrections

Igor Shenderovich

TL;DR

The work studies giant magnons in $AdS_4 \times CP^3$ using an algebraic-curve approach to derive both infinite-volume dispersion relations for two magnon types and finite-size, one-loop corrections. It shows that the one-loop correction vanishes in infinite volume, implying there is no constant term in the strong-coupling interpolating function $h(\lambda)$, and computes the first nonzero finite-size corrections which scale as $e^{-(E+L)/(4g)}$ with polarization-dependent coefficients. The results provide a nontrivial cross-check for the $AdS_4 \times CP^3$ S-matrix and deepen understanding of holographic integrability in the $AdS_4/CFT_3$ context. These findings illuminate how finite-size effects and quantum fluctuations constrain the spectrum and offer benchmarks for exact Bethe-ansatz and Lüscher-type analyses.

Abstract

We study giant magnon solutions in AdS4 \times CP3. We compute quantum corrections to their dispersion relation. We find out that the one--loop correction vanishes in infinite volume. This implies that the interpolating function h(λ) between strong and weak coupling regimes does not have a constant term λ^0 at strong coupling. We also compute first nonvanishing finite volume correction to the one--loop expression. When compared to the Lüsher formula, our results could provide a nontrivial check of the AdS4 \times CP3 S--matrix proposed recently in arXiv:0807.1924.

Giant magnons in AdS_4/CFT_3: dispersion, quantization and finite--size corrections

TL;DR

The work studies giant magnons in using an algebraic-curve approach to derive both infinite-volume dispersion relations for two magnon types and finite-size, one-loop corrections. It shows that the one-loop correction vanishes in infinite volume, implying there is no constant term in the strong-coupling interpolating function , and computes the first nonzero finite-size corrections which scale as with polarization-dependent coefficients. The results provide a nontrivial cross-check for the S-matrix and deepen understanding of holographic integrability in the context. These findings illuminate how finite-size effects and quantum fluctuations constrain the spectrum and offer benchmarks for exact Bethe-ansatz and Lüscher-type analyses.

Abstract

We study giant magnon solutions in AdS4 \times CP3. We compute quantum corrections to their dispersion relation. We find out that the one--loop correction vanishes in infinite volume. This implies that the interpolating function h(λ) between strong and weak coupling regimes does not have a constant term λ^0 at strong coupling. We also compute first nonvanishing finite volume correction to the one--loop expression. When compared to the Lüsher formula, our results could provide a nontrivial check of the AdS4 \times CP3 S--matrix proposed recently in arXiv:0807.1924.

Paper Structure

This paper contains 10 sections, 44 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Magnons: algebraic curve, quasimomenta and dispersion
  3. Giant magnon
  4. "Big" giant magnon
  5. Local charges
  6. GM quantization
  7. Finite size GM: one-loop corrections
  8. Conclusion
  9. Acknowledgments
  10. Twists computation

Figures (1)

  • Figure 1: Left picture corresponds to usual GM and the right one --- to a "big" GM solution. Red lines correspond to a pole, yellow --- to a log cut.