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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| Language: | English |
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2025-04-01
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| 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. |
| format | Article |
| id | doaj-art-155a32eb162440e9907178df3e6470dd |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| 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 |