Real and Virtual Bound States in Lüscher Corrections for CP3 Magnons

Abstract

We study classical and quantum finite-size corrections to giant magnons in AdS_4 x CP^3 using generalised Lüscher formulae. Lüscher F-terms are organised in powers of the exponential suppression factor exp(-Delta/2h)^m, and we calculate all terms in this series, matching one-loop algebraic curve results from our previous paper arXiv:1006.2174. Starting with the second term, the structure of these terms is different to those in AdS_5 x S^5 thanks to the appearance of heavy modes in the loop, which can here be interpreted as two-particle bound states in the mirror theory. By contrast, physical bound states can represent dyonic giant magnons, and we also calculate F-terms for these solutions. Lüscher mu-terms, suppressed by exp(-Delta/E), instead give at leading order the classical finite-size correction. For an elementary dyonic giant magnon, we recover the correction given by arXiv:0903.3365. We then extend this to calculate the next term in 1/h, giving a one-loop prediction. Finally we also calculate F-terms for the various composite giant magnons, RP^3 and `big', again finding agreement to all orders.

33 pages and 3 figures. v3 adds new section treating F-terms of all orders; version to appear in J. Phys. A

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Cited by in corpus (5)

• Massless Lüscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz
• Lectures on S-matrices and Integrability
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• An improved AFS phase for AdS3 string integrability
• Multi-Spin Strings in AdS_4*CP^3 and its β-deformation