Precision Test of AdS/CFT in Lunin-Maldacena Background

TL;DR

This paper tests the AdS/CFT correspondence by comparing semiclassical string solutions in the Lunin-Maldacena background with dual gauge theory operators, finding a precise match in their computed anomalous dimensions.

Contribution

It provides explicit solutions and energy calculations for two-spin semiclassical strings in the eta-deformed background, confirming the AdS/CFT correspondence in this setting.

Findings

Exact energy calculations for string states match gauge theory anomalous dimensions.

Identification of parameters between string theory and gauge theory is clarified.

Virasoro constraint interpretation enhances understanding of string-winding effects.

Abstract

We obtain the solutions and explicitly calculate the energy for a class of two-spin semiclassical string states in the Lunin-Maldacena background. These configurations are \beta-deformed versions of the folded string solutions in AdS_{5}\times S^{5} background. They correspond to certain single trace operators in the \mathcal{N}=1 superconformal \beta deformation of \mathcal{N}=4 Yang-Mills. We calculate the one loop anomalous dimension for the dual single trace operator from the associated twisted spin chain with a general two-cut distribution of Bethe roots. Our results show a striking match between the two calculations. We demonstrate the natural identification of parameters on the two sides of the analysis, and explain the significance of the Virasoro constraint associated with the winding motion of semiclassical strings from the perspective of the spin chain solution.