Worldsheet \(S\)-matrix of \(\beta\)-deformed SYM. (English) Zbl 1370.81138
Summary: We compute perturbative worldsheet \(S\)-matrix elements in the bosonic sector for \(\beta\)-deformed AdS/CFT in strong and weak ’t Hooft coupling limits and compare these with the exact \(S\)-matrix. For our purpose we take near BMN limit of \(\mathrm {TsT}\)-transformed \(\operatorname{AdS}_5 \times \mathrm S^5\) 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 \(\mathrm {SU}(3)\) 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 \(\beta\)-deformed AdS/CFT along with the appropriate twisted boundary conditions.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
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