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We study the null-polygonal minimal surfaces in AdS_4, which correspond tothe gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory atstrong coupling. The area of the minimal surfaces with n cusps is characterizedby the thermodynamic Bethe ansatz (TBA) integral equations or the Y-system ofthe homogeneous sine-Gordon model, which is regarded as theSU(n-4)_4/U(1)^{n-5} generalized parafermion theory perturbed by theweight-zero adjoint operators. Based on the relation to the TBA systems of theperturbed W minimal models, we solve the TBA equations by using the conformalperturbation theory, and obtain the analytic expansion of the remainderfunction around the UV/regular-polygonal limit for n=6 and 7. We compare therescaled remainder function for n=6 with the two-loop one, to observe that theyare close to each other similarly to the AdS_3 case.

Null-polygonal minimal surfaces in AdS_4 from perturbed W minimal models