Rotating Strings with Two Unequal Spins in Lunin-Maldacena Background

TL;DR

This paper analyzes rotating string solutions with two unequal spins in the eta-deformed AdS_5 imes ilde{S}^5 background, connecting string energies to gauge theory anomalous dimensions and providing loop corrections.

Contribution

It constructs explicit rotating string solutions with two unequal spins in the eta-deformed background and derives their energy corrections, linking them to gauge theory results.

Findings

Derived string energy in terms of spins and deformation parameter.

Matched one-loop string energy correction with gauge theory anomalous dimension.

Provided two-loop energy corrections for the string solutions.

Abstract

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-deformation of \mathcal{N} = 4 super Yang-Mills theory. For real \beta we 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 \lambda/J^2 with the total spin J and the string tension \sqrt{\lambda} 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 \beta-deformed Bethe equation as well as the anisotropic Landau-Lifshitz equation.