Extremal correlators and random matrix theory
Abstract We study the correlation functions of Coulomb branch operators of four-dimensional N $$ \mathcal{N} $$ = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2021)214 |
| _version_ | 1828941703602503680 |
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| author | Alba Grassi Zohar Komargodski Luigi Tizzano |
| author_facet | Alba Grassi Zohar Komargodski Luigi Tizzano |
| author_sort | Alba Grassi |
| collection | DOAJ |
| description | Abstract We study the correlation functions of Coulomb branch operators of four-dimensional N $$ \mathcal{N} $$ = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds. |
| first_indexed | 2024-12-14T03:41:02Z |
| format | Article |
| id | doaj.art-5a1a88f9be784f4fa63a7254cd1ab542 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T03:41:02Z |
| publishDate | 2021-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-5a1a88f9be784f4fa63a7254cd1ab5422022-12-21T23:18:29ZengSpringerOpenJournal of High Energy Physics1029-84792021-04-012021413810.1007/JHEP04(2021)214Extremal correlators and random matrix theoryAlba Grassi0Zohar Komargodski1Luigi Tizzano2Simons Center for Geometry and Physics, SUNYSimons Center for Geometry and Physics, SUNYSimons Center for Geometry and Physics, SUNYAbstract We study the correlation functions of Coulomb branch operators of four-dimensional N $$ \mathcal{N} $$ = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.https://doi.org/10.1007/JHEP04(2021)214Matrix ModelsNonperturbative EffectsSupersymmetric Gauge Theory |
| spellingShingle | Alba Grassi Zohar Komargodski Luigi Tizzano Extremal correlators and random matrix theory Journal of High Energy Physics Matrix Models Nonperturbative Effects Supersymmetric Gauge Theory |
| title | Extremal correlators and random matrix theory |
| title_full | Extremal correlators and random matrix theory |
| title_fullStr | Extremal correlators and random matrix theory |
| title_full_unstemmed | Extremal correlators and random matrix theory |
| title_short | Extremal correlators and random matrix theory |
| title_sort | extremal correlators and random matrix theory |
| topic | Matrix Models Nonperturbative Effects Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP04(2021)214 |
| work_keys_str_mv | AT albagrassi extremalcorrelatorsandrandommatrixtheory AT zoharkomargodski extremalcorrelatorsandrandommatrixtheory AT luigitizzano extremalcorrelatorsandrandommatrixtheory |