TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
Hao Ouyang (Center for Theoretical Physics and College of Physics, Jilin University, Changchun, 130012, China); Hongfei Shu (Yau Mathematical Sciences Center (YMSC), Tsinghua University, Beijing, 100084, China, Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, 101408, China)
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 $$ \mathcal{N} $$ = 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.
