Real and virtual bound states in Luscher corrections for CP super(3) magnons

We study classical and quantum finite-size corrections to giant magnons in AdS sub(4) x CP super(3) using generalized Luscher formulae. Luscher F-terms are organized in powers of the exponential suppression factor (e super(- Delta /2h)) super(m), and we calculate all terms in this series, matching one-loop algebraic curve results from our previous paper [1]. Starting with the second term, the structure of these terms is different to those in AdS sub(5) x S super(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. Luscher mu -terms, suppressed by e super(- Delta /E), instead give at leading order the classical finite-size correction. For the elementary dyonic giant magnon we recover the correction given by [2]. 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 super(3) and 'big', again finding agreement to all orders.