Worldsheet S-matrix of beta-deformed SYM

TL;DR

This paper computes the worldsheet S-matrix for beta-deformed AdS/CFT at different coupling regimes, comparing perturbative results with the conjectured exact S-matrix to validate the integrability of the deformed theory.

Contribution

It provides a detailed perturbative calculation of the worldsheet S-matrix in the beta-deformed setting and supports the conjecture of an exact S-matrix in this context.

Findings

Perturbative S-matrix matches the conjectured exact S-matrix at leading order.

Supports integrability of beta-deformed AdS/CFT with twisted boundary conditions.

Demonstrates consistency of weak and strong coupling analyses.

Abstract

We compute perturbative worldsheet S-matrix of beta-deformed AdS/CFT in the strong and weak `t Hooft coupling limit to compare with exact S-matrix. For the purpose we take near BMN limit of TsT-transformed AdS_5 x 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 the SU(3) sector by applying coordinate Bethe ansatz method to the 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 appropriate twisted boundary conditions.