Rotating Strings with Two Unequal Spins in Lunin-Maldacena Background

Abstract

We study a string motion in the Lunin-Maldacena background, that is, the β-deformed AdS_5 \times \tilde{S}^5 background dual to a β-deformation of \mathcal{N} = 4 super Yang-Mills theory. For real βwe construct a rotating 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 and the deformation parameter. In the expansion of λ/J^2 with the total spin J and the string tension \sqrtλ we present ``one-loop" and ``two-loop" energy corrections. The ``one-loop" one agrees with the one-loop anomalous dimension of the corresponding gauge-theory scalar operators obtained in hep-th/0503192 from the β-deformed Bethe equation as well as the anisotropic Landau-Lifshitz equation.