The anatomy of gauge/string duality in Lunin-Maldacena background

We consider the correspondence between the spinning string solutions in Lunin-Maldacena background and the single trace operators in the Leigh-Strassler deformation of N = 4 SYM. By imposing an appropriate rotating string ansaetz on the Landau-Lifshitz reduced sigma model in the deformed SU(2) sector, we find two types of 'elliptic' solutions with two spins, which turn out to be the solutions associated with the Neumann-Rosochatius system. We then calculate the string energies as functions of spins, and obtain their explicit forms in terms of a set of moduli parameters. On the deformed spin-chain side, we explicitly compute the one-loop anomalous dimensions of the gauge theory operators dual to each of the two types of spinning string solutions, extending and complementing the results of hep-th/0511164. Moreover, we propose explicit ansaetz on how the locations of the Bethe strings are affected due to the deformation, with several supports from the string side