Abstract
We study the null-polygonal minimal surfaces in AdS4, which correspond to the gluon scattering amplitudes/Wilson loops in \( \mathcal{N} \) = 4 super Yang-Mills theory at strong coupling. The area of the minimal surfaces with n cusps is characterized by the thermodynamic Bethe ansatz (TBA) integral equations or the Y-system of the homogeneous sine-Gordon model, which is regarded as the SU(n − 4)4 /U(1)n−5 generalized parafermion theory perturbed by the weight-zero adjoint operators. Based on the relation to the TBA systems of the perturbed W minimal models, we solve the TBA equations by using the conformal perturbation theory, and obtain the analytic expansion of the remainder function around the UV/regular-polygonal limit for n = 6 and 7. We compare the rescaled remainder function for n = 6 with the two-loop one, to observe that they are close to each other similarly to the AdS3 case.
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Hatsuda, Y., Ito, K. & Satoh, Y. Null-polygonal minimal surfaces in AdS4 from perturbed W minimal models. J. High Energ. Phys. 2013, 67 (2013). https://doi.org/10.1007/JHEP02(2013)067
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DOI: https://doi.org/10.1007/JHEP02(2013)067