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We address the question about the exact form of the dispersion relation forlight-cone string excitations in string theory in AdS3 x S3 x T4 with mixed R-Rand NS-NS 3-form fluxes. The analogy with string theory in AdS5 x S5 suggeststhat in addition to the data provided by the perturbative near-BMN expansionand the symmetry algebra considerations there is also another source ofinformation about the dispersion relation -- the semiclassical giant magnonsolution. In earlier work in arXiv:1303.1037 and arXiv:1304.4099 it was foundthat the symmetry algebra constraints consistent with perturbative expansion donot completely determine the form of the dispersion relation. The aim of thepresent paper is to fix it by constructing a generalization of the known dyonicgiant magnon soliton on S3 to the presence of a non-zero NS-NS flux describedby a WZ term in the string action. We find that the angular momentum of thissoliton gets shifted by a term linear in world-sheet momentum. We also discussthe symmetry algebra of the string light-cone S-matrix and show that the exactdispersion relation, which should have the correct perturbative BMN andsemiclassical giant magnon limits, should also contain such a linear momentumterm. The simplicity of the resulting bound-state picture provides a strongargument in favour of this dispersion relation.

Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux