Exact results and Schur expansions in quiver Chern-Simons-matter theories
Abstract We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities. We also consider Wilson loops in ABJ(M) theories, distinguishing between typica...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2020)022 |
| _version_ | 1819071312186834944 |
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| author | Leonardo Santilli Miguel Tierz |
| author_facet | Leonardo Santilli Miguel Tierz |
| author_sort | Leonardo Santilli |
| collection | DOAJ |
| description | Abstract We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities. We also consider Wilson loops in ABJ(M) theories, distinguishing between typical (long) and atypical (short) representations and focusing on the former. Using the Berele-Regev factorization of supersymmetric Schur polynomials, we express the expectation value of the Wilson loops in terms of sums of observables of two factorized copies of U(N ) pure Chern-Simons theory on the sphere. Then, we use the Cauchy identity to study the partition functions of a number of quiver Chern-Simons-matter models and the result is interpreted as a perturbative expansion in the parameters t j = −e 2πmj , where m j are the masses. Through the paper, we incorporate different generalizations, such as deformations by real masses and/or Fayet-Iliopoulos parameters, the consideration of a Romans mass in the gravity dual, and adjoint matter. |
| first_indexed | 2024-12-21T17:19:50Z |
| format | Article |
| id | doaj.art-e9c6477bbfb94f23a4058dc61ee2e0f0 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T17:19:50Z |
| publishDate | 2020-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e9c6477bbfb94f23a4058dc61ee2e0f02022-12-21T18:56:12ZengSpringerOpenJournal of High Energy Physics1029-84792020-10-0120201017110.1007/JHEP10(2020)022Exact results and Schur expansions in quiver Chern-Simons-matter theoriesLeonardo Santilli0Miguel Tierz1Grupo de Física Matemática, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo GrandeGrupo de Física Matemática, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo GrandeAbstract We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities. We also consider Wilson loops in ABJ(M) theories, distinguishing between typical (long) and atypical (short) representations and focusing on the former. Using the Berele-Regev factorization of supersymmetric Schur polynomials, we express the expectation value of the Wilson loops in terms of sums of observables of two factorized copies of U(N ) pure Chern-Simons theory on the sphere. Then, we use the Cauchy identity to study the partition functions of a number of quiver Chern-Simons-matter models and the result is interpreted as a perturbative expansion in the parameters t j = −e 2πmj , where m j are the masses. Through the paper, we incorporate different generalizations, such as deformations by real masses and/or Fayet-Iliopoulos parameters, the consideration of a Romans mass in the gravity dual, and adjoint matter.http://link.springer.com/article/10.1007/JHEP10(2020)022Matrix ModelsField Theories in Lower DimensionsChern-Simons TheoriesSupersymmetric Gauge Theory |
| spellingShingle | Leonardo Santilli Miguel Tierz Exact results and Schur expansions in quiver Chern-Simons-matter theories Journal of High Energy Physics Matrix Models Field Theories in Lower Dimensions Chern-Simons Theories Supersymmetric Gauge Theory |
| title | Exact results and Schur expansions in quiver Chern-Simons-matter theories |
| title_full | Exact results and Schur expansions in quiver Chern-Simons-matter theories |
| title_fullStr | Exact results and Schur expansions in quiver Chern-Simons-matter theories |
| title_full_unstemmed | Exact results and Schur expansions in quiver Chern-Simons-matter theories |
| title_short | Exact results and Schur expansions in quiver Chern-Simons-matter theories |
| title_sort | exact results and schur expansions in quiver chern simons matter theories |
| topic | Matrix Models Field Theories in Lower Dimensions Chern-Simons Theories Supersymmetric Gauge Theory |
| url | http://link.springer.com/article/10.1007/JHEP10(2020)022 |
| work_keys_str_mv | AT leonardosantilli exactresultsandschurexpansionsinquiverchernsimonsmattertheories AT migueltierz exactresultsandschurexpansionsinquiverchernsimonsmattertheories |