From Fredholm Determinants to AdS/CFT Observables: A Universal Strong-Coupling Framework
Abstract
We investigate the trans-series structure of the cusp anomalous dimension of 𝒩=4 supersymmetric Yang-Mills theory and the dynamically generated mass gap of the O(6) sigma model at strong 't Hooft coupling. We consider the one-parameter deformation of the cusp anomalous dimension, known as the tilted cusp, and review its strong-coupling expansion obtained through its representation in terms of Fredholm determinants with a matrix Bessel kernel. The advantage of this deformation is that the non-perturbative scales separate naturally, revealing structures that remain hidden in the physical limit. Motivated by this observation, we introduce the tilted mass gap, which reduces to the physical O(6) mass gap at a special value of the deformation parameter and exhibits a deep connection with the tilted cusp. This formulation allows us to determine the complete strong-coupling trans-series and resurgence structure of the O(6) mass gap, while extending and proving conjectured relations between successive non-perturbative corrections. Building on the underlying Fredholm determinant representation, we construct an Alien calculus that generates all non-perturbative sectors of these AdS/CFT observables directly from their perturbative expansions. Finally, we derive an exact all-orders relation between the strong-coupling trans-series of the O(6) mass gap and the cusp anomalous dimension of planar 𝒩=4 supersymmetric Yang-Mills theory.
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BibTeX
@misc{boldis2026from,
title = {{From Fredholm Determinants to AdS/CFT Observables: A Universal Strong-Coupling Framework}},
author = {Bercel Boldis and Dennis le Plat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.13140},
eprint = {2607.13140},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.13140},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Fredholm Determinants to AdS/CFT Observables: A Universal Strong-Coupling Framework
AU - Bercel Boldis
AU - Dennis le Plat
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2607.13140
UR - https://arxiv.org/abs/2607.13140
AB - We investigate the trans-series structure of the cusp anomalous dimension of 𝒩=4 supersymmetric Yang-Mills theory and the dynamically generated mass gap of the O(6) sigma model at strong 't Hooft coupling. We consider the one-parameter deformation of the cusp anomalous dimension, known as the tilted cusp, and review its strong-coupling expansion obtained through its representation in terms of Fredholm determinants with a matrix Bessel kernel. The advantage of this deformation is that the non-perturbative scales separate naturally, revealing structures that remain hidden in the physical limit. Motivated by this observation, we introduce the tilted mass gap, which reduces to the physical O(6) mass gap at a special value of the deformation parameter and exhibits a deep connection with the tilted cusp. This formulation allows us to determine the complete strong-coupling trans-series and resurgence structure of the O(6) mass gap, while extending and proving conjectured relations between successive non-perturbative corrections. Building on the underlying Fredholm determinant representation, we construct an Alien calculus that generates all non-perturbative sectors of these AdS/CFT observables directly from their perturbative expansions. Finally, we derive an exact all-orders relation between the strong-coupling trans-series of the O(6) mass gap and the cusp anomalous dimension of planar 𝒩=4 supersymmetric Yang-Mills theory.
ER -