Abstract
Alday and Maldacena conjectured an equivalence between string amplitudes in and null polygonal Wilson loops in planar super-Yang-Mills (SYM) theory. At strong coupling this identifies SYM amplitudes with areas of minimal surfaces in anti–de Sitter space. For minimal surfaces in , we find that the nontrivial part of these amplitudes, the remainder function, satisfies an integrable system of nonlinear differential equations, and we give its Lax form. The result follows from a new perspective on “ systems,” which defines a new psuedo-hyper-Kähler structure directly on the space of kinematic data, via a natural twistor space defined by the -system equations. The remainder function is the (pseudo-)Kähler scalar for this geometry. This connection to pseudo-hyper-Kähler geometry and its twistor theory provides a new ingredient for extending recent conjectures for nonperturbative amplitudes using structures arising at strong coupling.
- Received 10 August 2023
- Revised 27 December 2023
- Accepted 18 March 2024
DOI:https://doi.org/10.1103/PhysRevLett.132.151603
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Published by the American Physical Society