Real and Virtual Bound States in L\"uscher Corrections for CP3 Magnons

TL;DR

This paper computes classical and quantum finite-size corrections to giant magnons in AdS_4 x CP^3 using generalized L"uscher formulas, revealing differences from AdS_5 x S^5 due to heavy modes and bound states.

Contribution

It provides a comprehensive calculation of all L"uscher F-terms and mu-terms for giant magnons in AdS_4 x CP^3, including bound states and one-loop predictions, extending previous results.

Findings

All terms in the exponential suppression series are calculated.

Heavy modes lead to different structures compared to AdS_5 x S^5.

Agreement with previous algebraic curve results and classical corrections.

Abstract

We study classical and quantum finite-size corrections to giant magnons in AdS_4 x CP^3 using generalised L\"uscher formulae. L\"uscher 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. L\"uscher 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.