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

Abstract

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 ansätz 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 ansätz on how the locations of the Bethe strings are affected due to the deformation, with several supports from the string side.

Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries

“…Therefore, just as in the undeformed case (reviewed in [17]) one can attempt to compare gauge theory results with strong coupling ones by considering semiclassical strings moving on the LM background. This was done in [18], with the construction of several semiclassical string solutions, which were matched to specific configurations of roots of the twisted Bethe ansatz. Their energies precisely agree with the gauge theory anomalous dimensions.…”

On the perturbative chiral ring for marginally deformed Script N=4 SYM theories

“…On the string theory side BPS states have been investigated in [32] for orbifold configurations. Integrability properties have been exploited on the two sides of the correspondence in order to match the energies of semiclassical fast rotating strings with one-loop anomalous dimensions of scalar operators [33,34,35,36,37]. The spectrum of states has been also investigated in the BMN limit [38,39].…”

A REVIEW OF INTEGRABLE DEFORMATIONS IN AdS/CFT

“…This problem was studied directly and indirectly, for example, in Refs. 11,12,13,14,15,16,17,18,19,20,21 (see also references therein). The dynamics of both theories can be captured, at least in certain limits, by twisted Bethe equations.…”