2023/06/29 by Frost, Hadleigh, Gürdogan, Ömer, Mason, Lionel
#Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2306.17044
Alday & Maldacena conjectured an equivalence between string amplitudes in AdS5 × S5 and null polygonal Wilson loops in planar N=4 super-Yang-Mills (SYM). At strong coupling this identifies SYM amplitudes with areas of minimal surfaces in AdS. For minimal surfaces in AdS3, 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 `Y-systems', which defines a new psuedo-hyperkähler structure directly on the space of kinematic data, via a natural twistor space defined by the Y-system equations. The remainder function is the (pseudo-)Kähler scalar for this geometry. This connection to pseudo-hyperkähler geometry and its twistor theory provides a new ingredient for extending recent conjectures for non-perturbative amplitudes using structures arising at strong coupling.