Amplitudes at strong coupling as Hyper-Kähler Scalars

Frost, Hadleigh, Gürdoğan, Ömer and Mason, Lionel (2024) Amplitudes at strong coupling as Hyper-Kähler Scalars. Physical Review Letters, 132 (15), [151603]. (doi:10.1103/PhysRevLett.132.151603).

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Abstract

Alday and Maldacena conjectured an equivalence between string amplitudes in AdS5×S5 and null polygonal Wilson loops in planar N=4 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 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-hyper-Kähler 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-hyper-Kähler geometry and its twistor theory provides a new ingredient for extending recent conjectures for nonperturbative amplitudes using structures arising at strong coupling.

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Accepted/In Press date: 18 March 2024

Published date: 12 April 2024

Additional Information: Publisher Copyright: © 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.