Rotating strings with two unequal spins in Lunin-Maldacena background

We study a string motion in the Lunin-Maldacena background, that is, the\beta-deformed AdS_5 \times \tilde{S}^5 background dual to a \beta-deformationof \mathcal{N} = 4 super Yang-Mills theory. For real \beta we construct arotating and wound string solution which has two unequal spins in \tilde{S}^5.The string energy is expressed in terms of the spins, the winding numbers andthe deformation parameter. In the expansion of \lambda/J^2 with the total spinJ and the string tension \sqrt{\lambda} we present ``one-loop" and ``two-loop"energy corrections. The ``one-loop" one agrees with the one-loop anomalousdimension of the corresponding gauge-theory scalar operators obtained inhep-th/0503192 from the \beta-deformed Bethe equation as well as theanisotropic Landau-Lifshitz equation.Comment: 13 pages, LaTeX, no figure