Non-perturbative defects in tensor models from melonic trees
Abstract The Klebanov-Tarnopolsky tensor model is a quantum field theory for rank-three tensor scalar fields with certain quartic potential. The theory possesses an unusual large N limit known as the melonic limit that is strongly coupled yet solvable, producing at large distance a rare example of n...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP11(2022)057 |
| _version_ | 1797865757738008576 |
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| author | Fedor K. Popov Yifan Wang |
| author_facet | Fedor K. Popov Yifan Wang |
| author_sort | Fedor K. Popov |
| collection | DOAJ |
| description | Abstract The Klebanov-Tarnopolsky tensor model is a quantum field theory for rank-three tensor scalar fields with certain quartic potential. The theory possesses an unusual large N limit known as the melonic limit that is strongly coupled yet solvable, producing at large distance a rare example of non-perturbative non-supersymmetric conformal field theory that admits analytic solutions. We study the dynamics of defects in the tensor model defined by localized magnetic field couplings on a p-dimensional subspace in the d-dimensional spacetime. While we work with general p and d, the physically interesting cases include line defects in d = 2, 3 and surface defects in d = 3. By identifying a novel large N limit that generalizes the melonic limit in the presence of defects, we prove that the defect one-point function of the scalar field only receives contributions from a subset of the Feynman diagrams in the shape of melonic trees. These diagrams can be resummed using a closed Schwinger-Dyson equation which enables us to determine non-perturbatively this defect one-point function. At large distance, the solutions we find describe nontrivial conformal defects and we discuss their defect renormalization group (RG) flows. In particular, for line defects, we solve the exact RG flow between the trivial and the conformal lines in d = 4 − ϵ. We also compute the exact line defect entropy and verify the g-theorem. Furthermore we analyze the defect two-point function of the scalar field and its decomposition via the operator-product-expansion, providing explicit formulae for one-point functions of bilinear operators and the stress-energy tensor. |
| first_indexed | 2024-04-09T23:13:22Z |
| format | Article |
| id | doaj.art-aac4c036145947aba748e0b5600fb540 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:13:22Z |
| publishDate | 2022-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-aac4c036145947aba748e0b5600fb5402023-03-22T10:15:09ZengSpringerOpenJournal of High Energy Physics1029-84792022-11-0120221113810.1007/JHEP11(2022)057Non-perturbative defects in tensor models from melonic treesFedor K. Popov0Yifan Wang1Center for Cosmology and Particle Physics, New York UniversityCenter for Cosmology and Particle Physics, New York UniversityAbstract The Klebanov-Tarnopolsky tensor model is a quantum field theory for rank-three tensor scalar fields with certain quartic potential. The theory possesses an unusual large N limit known as the melonic limit that is strongly coupled yet solvable, producing at large distance a rare example of non-perturbative non-supersymmetric conformal field theory that admits analytic solutions. We study the dynamics of defects in the tensor model defined by localized magnetic field couplings on a p-dimensional subspace in the d-dimensional spacetime. While we work with general p and d, the physically interesting cases include line defects in d = 2, 3 and surface defects in d = 3. By identifying a novel large N limit that generalizes the melonic limit in the presence of defects, we prove that the defect one-point function of the scalar field only receives contributions from a subset of the Feynman diagrams in the shape of melonic trees. These diagrams can be resummed using a closed Schwinger-Dyson equation which enables us to determine non-perturbatively this defect one-point function. At large distance, the solutions we find describe nontrivial conformal defects and we discuss their defect renormalization group (RG) flows. In particular, for line defects, we solve the exact RG flow between the trivial and the conformal lines in d = 4 − ϵ. We also compute the exact line defect entropy and verify the g-theorem. Furthermore we analyze the defect two-point function of the scalar field and its decomposition via the operator-product-expansion, providing explicit formulae for one-point functions of bilinear operators and the stress-energy tensor.https://doi.org/10.1007/JHEP11(2022)057Global SymmetriesNonperturbative EffectsRenormalization GroupScale and Conformal Symmetries |
| spellingShingle | Fedor K. Popov Yifan Wang Non-perturbative defects in tensor models from melonic trees Journal of High Energy Physics Global Symmetries Nonperturbative Effects Renormalization Group Scale and Conformal Symmetries |
| title | Non-perturbative defects in tensor models from melonic trees |
| title_full | Non-perturbative defects in tensor models from melonic trees |
| title_fullStr | Non-perturbative defects in tensor models from melonic trees |
| title_full_unstemmed | Non-perturbative defects in tensor models from melonic trees |
| title_short | Non-perturbative defects in tensor models from melonic trees |
| title_sort | non perturbative defects in tensor models from melonic trees |
| topic | Global Symmetries Nonperturbative Effects Renormalization Group Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP11(2022)057 |
| work_keys_str_mv | AT fedorkpopov nonperturbativedefectsintensormodelsfrommelonictrees AT yifanwang nonperturbativedefectsintensormodelsfrommelonictrees |