Abstract
We compute perturbative worldsheet S-matrix elements in the bosonic sector for β-deformed AdS/CFT in strong and weak ʼt Hooft coupling limits and compare with the exact S-matrix. For our purpose we take near BMN limit of TsT-transformed AdS5×S5 with the twisted boundary condition and compute the S-matrix on worldsheet using light-cone gauge fixed Lagrangian. For the weak coupling side, we compute the S-matrix in SU(3) sector by applying coordinate Bethe ansatz method to one-loop dilatation operator obtained from the deformed super Yang–Mills theory. These analysis support the conjectured exact S-matrix in the leading order for both sides of β-deformed AdS/CFT along with the appropriate twisted boundary conditions.
Highlights
The S-matrix plays a key role for studying two-dimensional integrable models
It is natural to extend the utility of the integrable methods to other proposed or conjectured AdS/CFT dualities. These include β-deformed super Yang-Mills theory (SYM) theory [9] which is dual to superstring theory on Lunin-Maldacena background [10] and three-parameter-deformed theory which breaks all the supersymmetry [11]
All-loop asymptotic Bethe ansatz equations for the deformed theories were conjectured by Beisert and Roiban [15]
Summary
The S-matrix plays a key role for studying two-dimensional integrable models. With enough symmetries, the S-matrix can be determined mathematically and can be used to find particle spectrum along with exact dispersion relations and to compute finite-size effects. Finite J correction of a classical giant magnon dispersion relation has been computed from the S-matrix element and twisted boundary conditions through Luscher formula [20] and shown to match with classical sigma model computation for the γ-deformed background [21, 22] While these evidences justify the assumption of integrability, it is desirable to check the S-matrix directly either with the string theory on a deformed background in the strong coupling limit or with the N = 1 supersymmetric or non-supersymmetric gauge theories in the weak coupling limit. We study the S-matrix of the β-deformed SYM at strong and weak ’t Hooft coupling regimes which corresponds to (1.1) where the boundary condition (1.2) becomes a c-number For this purpose, we consider string world-sheet action in near BMN limit and with light-cone gauge fixing which is different from Lunin-Maldacena and compute the worldsheet scattering as was done for untwisted case in [24]. We apply coordinate Bethe ansatz to compute one-loop S-matrix in this sector using the deformed SU(3) spin chain Hamiltonian derived in [14, 25] and show that it matches with the exact Drinfeld-Reshetikhin S-matrix (1.1) in this limit
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