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arXiv · 2306.17044

Amplitudes at strong coupling as hyperkähler scalars

Hadleigh Frost·Ömer Gürdogan·Lionel Mason
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Abstract

Alday & Maldacena conjectured an equivalence between string amplitudes in AdS$_5 \times S^5$ and null polygonal Wilson loops in planar $\mathcal{N}=4$ super-Yang-Mills (SYM). At strong coupling this identifies SYM amplitudes with areas of minimal surfaces in AdS. For minimal surfaces in AdS$_3$, we find that the nontrivial part of these amplitudes, the \emph{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 \emph{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.

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Hadleigh Frost, Ömer Gürdogan, Lionel Mason. 2023-12-27. Amplitudes at strong coupling as hyperkähler scalars. https://arxiv.org/abs/2306.17044

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