Solving four-dimensional superconformal Yang-Mills theories with Tracy-Widom distribution

Abstract We study a special class of observables in N $$ \mathcal{N} $$ = 2 and N $$ \mathcal{N} $$ = 4 superconformal Yang-Mills theories which, for an arbitrary ’t Hooft coupling constant λ, admit representation as determinants of certain semi-infinite matrices. Similar determinants have previousl...

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Main Authors: Zoltan Bajnok, Bercel Boldis, Gregory P. Korchemsky
Format: Article
Language:English
Published: SpringerOpen 2025-04-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP04(2025)005
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author Zoltan Bajnok
Bercel Boldis
Gregory P. Korchemsky
author_facet Zoltan Bajnok
Bercel Boldis
Gregory P. Korchemsky
author_sort Zoltan Bajnok
collection DOAJ
description Abstract We study a special class of observables in N $$ \mathcal{N} $$ = 2 and N $$ \mathcal{N} $$ = 4 superconformal Yang-Mills theories which, for an arbitrary ’t Hooft coupling constant λ, admit representation as determinants of certain semi-infinite matrices. Similar determinants have previously appeared in the study of level-spacing distributions in random matrices and are closely related to the celebrated Tracy-Widom distribution. We exploit this relationship to develop an efficient method for computing the observables in superconformal Yang-Mills theories at both weak and strong coupling. The weak coupling expansion has a finite radius of convergence. The strong coupling expansion involves the sum of the ‘perturbative’ part, given by series in 1/ λ $$ \sqrt{\lambda } $$ , and the ‘non-perturbative’ part, given by an infinite sum of exponentially small terms, each accompanied by a series in 1/ λ $$ \sqrt{\lambda } $$ with factorially growing coefficients. We explicitly compute the expansion coefficients of these series and show that they are uniquely determined by the large order behavior of the expansion coefficients of the perturbative part via resurgence relations.
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spelling doaj-art-155a32eb162440e9907178df3e6470dd2025-08-20T03:53:22ZengSpringerOpenJournal of High Energy Physics1029-84792025-04-012025414210.1007/JHEP04(2025)005Solving four-dimensional superconformal Yang-Mills theories with Tracy-Widom distributionZoltan Bajnok0Bercel Boldis1Gregory P. Korchemsky2HUN-REN Wigner Research Centre for PhysicsBudapest University of Technology and EconomicsInstitut de Physique Théorique (Unité Mixte de Recherche 3681 du CNRS), Université Paris Saclay, CNRSAbstract We study a special class of observables in N $$ \mathcal{N} $$ = 2 and N $$ \mathcal{N} $$ = 4 superconformal Yang-Mills theories which, for an arbitrary ’t Hooft coupling constant λ, admit representation as determinants of certain semi-infinite matrices. Similar determinants have previously appeared in the study of level-spacing distributions in random matrices and are closely related to the celebrated Tracy-Widom distribution. We exploit this relationship to develop an efficient method for computing the observables in superconformal Yang-Mills theories at both weak and strong coupling. The weak coupling expansion has a finite radius of convergence. The strong coupling expansion involves the sum of the ‘perturbative’ part, given by series in 1/ λ $$ \sqrt{\lambda } $$ , and the ‘non-perturbative’ part, given by an infinite sum of exponentially small terms, each accompanied by a series in 1/ λ $$ \sqrt{\lambda } $$ with factorially growing coefficients. We explicitly compute the expansion coefficients of these series and show that they are uniquely determined by the large order behavior of the expansion coefficients of the perturbative part via resurgence relations.https://doi.org/10.1007/JHEP04(2025)0051/N ExpansionAdS-CFT CorrespondenceExtended Supersymmetry
spellingShingle Zoltan Bajnok
Bercel Boldis
Gregory P. Korchemsky
Solving four-dimensional superconformal Yang-Mills theories with Tracy-Widom distribution
Journal of High Energy Physics
1/N Expansion
AdS-CFT Correspondence
Extended Supersymmetry
title Solving four-dimensional superconformal Yang-Mills theories with Tracy-Widom distribution
title_full Solving four-dimensional superconformal Yang-Mills theories with Tracy-Widom distribution
title_fullStr Solving four-dimensional superconformal Yang-Mills theories with Tracy-Widom distribution
title_full_unstemmed Solving four-dimensional superconformal Yang-Mills theories with Tracy-Widom distribution
title_short Solving four-dimensional superconformal Yang-Mills theories with Tracy-Widom distribution
title_sort solving four dimensional superconformal yang mills theories with tracy widom distribution
topic 1/N Expansion
AdS-CFT Correspondence
Extended Supersymmetry
url https://doi.org/10.1007/JHEP04(2025)005
work_keys_str_mv AT zoltanbajnok solvingfourdimensionalsuperconformalyangmillstheorieswithtracywidomdistribution
AT bercelboldis solvingfourdimensionalsuperconformalyangmillstheorieswithtracywidomdistribution
AT gregorypkorchemsky solvingfourdimensionalsuperconformalyangmillstheorieswithtracywidomdistribution