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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.05805 |
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| _version_ | 1866910770060591104 |
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| author | Kade, Moritz Staudacher, Matthias |
| author_facet | Kade, Moritz Staudacher, Matthias |
| contents | We consider the double scaling limit of $β$-deformed planar N = 4 supersymmetric Yang-Mills theory (SYM), which has been argued to be conformal and integrable. It is a special point in the three-parameter space of double-scaled $γ_i$-deformed N = 4 SYM, preserving N = 1 supersymmetry. The Feynman diagrams of the general three-parameter models form a "dynamical fishnet" that is much harder to analyze than the original one-parameter fishnet, where major progress in uncovering the model's integrable structure has been made in recent years. Here we show that by applying N = 1 superspace techniques to the $β$-deformed model the dynamical nature of its Feynman graph expansion disappears, and we recover a regular lattice structure of brick wall (honeycomb) type. As a first application, we compute the zero-mode-fixed thermodynamic free energy of this model by applying Zamolodchikov's method of inversion to the supersymmetric brick wall diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supersymmetric brick wall diagrams and the dynamical fishnet Kade, Moritz Staudacher, Matthias High Energy Physics - Theory We consider the double scaling limit of $β$-deformed planar N = 4 supersymmetric Yang-Mills theory (SYM), which has been argued to be conformal and integrable. It is a special point in the three-parameter space of double-scaled $γ_i$-deformed N = 4 SYM, preserving N = 1 supersymmetry. The Feynman diagrams of the general three-parameter models form a "dynamical fishnet" that is much harder to analyze than the original one-parameter fishnet, where major progress in uncovering the model's integrable structure has been made in recent years. Here we show that by applying N = 1 superspace techniques to the $β$-deformed model the dynamical nature of its Feynman graph expansion disappears, and we recover a regular lattice structure of brick wall (honeycomb) type. As a first application, we compute the zero-mode-fixed thermodynamic free energy of this model by applying Zamolodchikov's method of inversion to the supersymmetric brick wall diagrams. |
| title | Supersymmetric brick wall diagrams and the dynamical fishnet |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2408.05805 |