Giant Wilson loops from Fredholm determinants

Ludvig Chen; Victor Mishnyakov; Konstantin Zarembo

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arXiv · 2610.20493

Giant Wilson loops from Fredholm determinants

Ludvig Chen·Victor Mishnyakov·Konstantin Zarembo

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Abstract

We study large-k symmetric and antisymmetric Wilson loops in N=4 super-Yang-Mills theory. We represent their generating functions as Fredholm determinants built from the Hermite kernel weighted by a symbol function that encodes the representation. Using the integrable structure of the kernel, we systematically apply the Tracy-Widom approach to derive a closed system of integro-differential equations. The equations are then solved order by order in 1/N by a WKB ansatz, while keeping the symbol function general. We find a closed-form expression for the leading and subleading order contributions to the generating functions. Finally, specializing to the two representations, we perform the large-k saddle-point analysis and find the subleading contribution to the Wilson loop. Our results confirm the previously observed discrepancies with the dual D-brane description of giant Wilson loops.

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BibTeX RIS

Ludvig Chen, Victor Mishnyakov, Konstantin Zarembo. 2026-10-14. Giant Wilson loops from Fredholm determinants. https://arxiv.org/abs/2610.20493

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