Finite-size effects for dyonic giant magnons Original Research Article

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, ] 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, ] to the situation in which incoming particles are boundstates. By careful choice of poles in the image-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 ʹt Hooft coupling.