Giant Wilson loops from Fredholm determinants
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.
Related
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BibTeX
@misc{chen2026giant,
title = {{Giant Wilson loops from Fredholm determinants}},
author = {Ludvig Chen and Victor Mishnyakov and Konstantin Zarembo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20493},
eprint = {2610.20493},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20493},
}
RIS
TY - UNPB
TI - Giant Wilson loops from Fredholm determinants
AU - Ludvig Chen
AU - Victor Mishnyakov
AU - Konstantin Zarembo
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.20493
UR - https://arxiv.org/abs/2610.20493
AB - 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.
ER -