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Gauge/string duality and thermodynamic Bethe ansatz equations

We review recent developments in the study of gluon scattering amplitudes of the four-dimensional maximally supersymmetric Yang-Mills theory at strong coupling based on the gauge/string duality and its underlying integrability. The scattering amplitudes are given by the area of minimal surfaces in five-dimensional anti-de Sitter space with a null polygonal boundary. These minimal surfaces are described by integral equations of the form of the thermodynamic Bethe ansatz equations. Generalizing the result regarding the six-point amplitudes, we observe a general connection between the minimal surfaces and the homogenous sine-Gordon model, which is a class of two-dimensional integrable models associated with certain coset conformal field theories. We also demonstrate that the identification of the underlying integrable models is useful for analyzing the amplitudes by explicitly deriving an expansion of the six-point amplitudes around a special kinematic point.