Journal of High Energy Physics (May 2022)
TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
Abstract
Abstract We compute the minimal area of a string worldsheet ending on two infinite periodic light-like Wilson lines in the AdS3 boundary, which is dual to the first non-planar correction to the gluon scattering amplitude in N $$ \mathcal{N} $$ = 4 SYM at the strong coupling. Using the connection between the Hitchin system and the thermodynamic Bethe ansatz (TBA) equations, we present an analytic method to compute the minimal area surface and express the non-trivial part of the minimal area in terms of the free energy of the TBA-like equations. Given the cross ratios as inputs, the area computed from the TBA-like equations matches that calculated using the numerical integration.
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