The coupling flow of N $$ \mathcal{N} $$ = 4 super Yang-Mills theory
Abstract We offer a novel perspective on N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills (SYM) theory through the framework of the Nicolai map, a transformation of the bosonic fields that allows one to compute quantum correlators in terms of a free, purely bosonic functional measure. Generally, an...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP04(2022)004 |
| _version_ | 1797865800401420288 |
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| author | Maximilian Rupprecht |
| author_facet | Maximilian Rupprecht |
| author_sort | Maximilian Rupprecht |
| collection | DOAJ |
| description | Abstract We offer a novel perspective on N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills (SYM) theory through the framework of the Nicolai map, a transformation of the bosonic fields that allows one to compute quantum correlators in terms of a free, purely bosonic functional measure. Generally, any Nicolai map is obtained through a path-ordered exponential of the so-called coupling flow operator. The latter can be canonically constructed in any gauge using an N $$ \mathcal{N} $$ = 1 off-shell superfield formulation of N $$ \mathcal{N} $$ = 4 SYM, or alternatively through dimensional reduction of the result from N $$ \mathcal{N} $$ = 1 D = 10 SYM, in which case we need to restrict to the Landau gauge. We propose a general theory of the N $$ \mathcal{N} $$ = 4 coupling flow operator, arguing that it exhibits an ambiguity in form of an R-symmetry freedom given by the Lie algebra su $$ \mathfrak{su} $$ (4). This theory incorporates our two construction approaches as special points in su $$ \mathfrak{su} $$ (4) and defines a broad class of Nicolai maps for N $$ \mathcal{N} $$ = 4 SYM. |
| first_indexed | 2024-04-09T23:14:18Z |
| format | Article |
| id | doaj.art-91de63ff99124d549e3a5ab6fa8f234c |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:14:18Z |
| publishDate | 2022-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-91de63ff99124d549e3a5ab6fa8f234c2023-03-22T10:11:30ZengSpringerOpenJournal of High Energy Physics1029-84792022-04-012022413910.1007/JHEP04(2022)004The coupling flow of N $$ \mathcal{N} $$ = 4 super Yang-Mills theoryMaximilian Rupprecht0Institut für Theoretische Physik and Riemann Center for Geometry and Physics, Leibniz Universität HannoverAbstract We offer a novel perspective on N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills (SYM) theory through the framework of the Nicolai map, a transformation of the bosonic fields that allows one to compute quantum correlators in terms of a free, purely bosonic functional measure. Generally, any Nicolai map is obtained through a path-ordered exponential of the so-called coupling flow operator. The latter can be canonically constructed in any gauge using an N $$ \mathcal{N} $$ = 1 off-shell superfield formulation of N $$ \mathcal{N} $$ = 4 SYM, or alternatively through dimensional reduction of the result from N $$ \mathcal{N} $$ = 1 D = 10 SYM, in which case we need to restrict to the Landau gauge. We propose a general theory of the N $$ \mathcal{N} $$ = 4 coupling flow operator, arguing that it exhibits an ambiguity in form of an R-symmetry freedom given by the Lie algebra su $$ \mathfrak{su} $$ (4). This theory incorporates our two construction approaches as special points in su $$ \mathfrak{su} $$ (4) and defines a broad class of Nicolai maps for N $$ \mathcal{N} $$ = 4 SYM.https://doi.org/10.1007/JHEP04(2022)004Extended SupersymmetrySupersymmetric Gauge TheoryGlobal Symmetries |
| spellingShingle | Maximilian Rupprecht The coupling flow of N $$ \mathcal{N} $$ = 4 super Yang-Mills theory Journal of High Energy Physics Extended Supersymmetry Supersymmetric Gauge Theory Global Symmetries |
| title | The coupling flow of N $$ \mathcal{N} $$ = 4 super Yang-Mills theory |
| title_full | The coupling flow of N $$ \mathcal{N} $$ = 4 super Yang-Mills theory |
| title_fullStr | The coupling flow of N $$ \mathcal{N} $$ = 4 super Yang-Mills theory |
| title_full_unstemmed | The coupling flow of N $$ \mathcal{N} $$ = 4 super Yang-Mills theory |
| title_short | The coupling flow of N $$ \mathcal{N} $$ = 4 super Yang-Mills theory |
| title_sort | coupling flow of n mathcal n 4 super yang mills theory |
| topic | Extended Supersymmetry Supersymmetric Gauge Theory Global Symmetries |
| url | https://doi.org/10.1007/JHEP04(2022)004 |
| work_keys_str_mv | AT maximilianrupprecht thecouplingflowofnmathcaln4superyangmillstheory AT maximilianrupprecht couplingflowofnmathcaln4superyangmillstheory |