×

\(Y\)-system for scattering amplitudes. (English) Zbl 1204.81134

Summary: We compute \(\mathcal N = 4\) super Yang-Mills planar amplitudes at strong coupling by considering minimal surfaces in AdS\(_{5}\) space. The surfaces end on a null polygonal contour at the boundary of AdS. We show how to compute the area of the surfaces as a function of the conformal cross ratios characterizing the polygon at the boundary. We reduce the problem to a simple set of functional equations for the cross ratios as functions of the spectral parameter. These equations have the form of thermodynamic Bethe ansatz (TBA) equations. The area is the free energy of the TBA system. We consider any number of gluons and any kinematic configuration.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81U05 \(2\)-body potential quantum scattering theory
81T13 Yang-Mills and other gauge theories in quantum field theory
PDFBibTeX XMLCite
Full Text: DOI arXiv