Finite-size effects for dyonic giant magnons

We compute finite-size corrections to dyonic giant magnons in two ways. One is by examining the asymptotic behavior of helical strings of [K. Okamura, R. Suzuki, A perspective on classical strings from complex sine-Gordon solitons, Phys. Rev. D 75 (2007) 046001, hep-th/0609026] as elliptic modulus k goes to unity, and the other is by applying the generalized Lüscher formula for μ-term of [R.A. Janik, T. Łukowski, Wrapping interactions at strong coupling—the giant magnon, Phys. Rev. D 76 (2007) 126008, arXiv: 0708.2208 [hep-th]] to the situation in which incoming particles are boundstates. By careful choice of poles in the su(2|2)2su(2|2)2-invariant S-matrix, we find agreement of the two results, which makes possible to predict the (leading) finite-size correction for dyonic giant magnons to all orders in the 't Hooft coupling.