Michael C. Abbott, Inês Aniceto, Diego Bombardelli
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 the second (m=2, or 'NLO') term in this series, matching a result
of our previous paper arXiv:1006.2174. The structure of this term is different
to that in AdS_5 x S^5 thanks to the appearance of heavy modes in the loop,
which can here be interpreted as bound states in the mirror theory. By
contrast, physical bound states give us corrections to dyonic giant magnons,
and we calculate F-terms for these, up to m=2 . 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 (up to
m=2) for the various composite giant magnons, RP^3 and 'big'.
View original:
http://arxiv.org/abs/1111.2839
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