 
Summary: Finitesize effect of the dyonic giant magnons in N ¼ 6 super ChernSimons theory
Changrim Ahn* and P. Bozhilov
Department of Physics Ewha Womans University DaeHyun 111, Seoul 120750, Republic of Korea
(Received 4 December 2008; published 19 February 2009)
We consider finitesize effects for the dyonic giant magnon of the type IIA string theory on AdS4 Â
CP3
by applying the Lu¨scher term formula which is derived from a recently proposed S matrix for the
N ¼ 6 super ChernSimons theory. We compute explicitly the effect for the case of a symmetric
configuration where the two external bound states, each of A and B particles, have the same momentum p
and spin J2. We compare this with the classical string theory result which we computed by reducing it to
the NeumannRosochatius system. The two results match perfectly.
DOI: 10.1103/PhysRevD.79.046008 PACS numbers: 11.25.Tq, 03.70.+k, 04.60.Cf
I. INTRODUCTION
The AdS/CFT correspondence between type IIB string
theory on AdS5 Â S5 and N ¼ 4 super YangMills
(SYM) theory [13] led to many exciting developments
and to understanding nonperturbative structures of the
string and gauge theories. Recently, an exciting possibility
that the same type of duality does exist in three
dimensional gauge theory has been discovered. The prom
