Multispin giant magnons

Abstract

We investigate giant magnons from classical rotating strings in two different backgrounds. First we generalize the solution of Hofman and Maldacena and investigate new magnon excitations of a spin chain which are dual to a string on $R\ifmmode\times\else\texttimes\fi{}{S}^{5}$ with two nonvanishing angular momenta. Allowing string dynamics along the third angle in the five sphere, we find a dispersion relation that reproduces the Hofman and Maldacena one and the one found by Dorey for the two spin case. In the second part of the paper we generalize the two ``spin'' giant magnon to the case of $\ensuremath{\beta}$-deformed ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ background. We find agreement between the dispersion relation of the rotating string and the proposed dispersion relation of the magnon bound state on the spin chain.