Hidden symmetries of 4D N $$ \mathcal{N} $$ = 2 gauge theories
Abstract We study the global symmetries of the ℤ 2-orbifold of N $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory and its marginal deformations. The process of orbifolding to obtain an N $$ \mathcal{N} $$ = 2 theory would appear to break the SU(4) R-symmetry down to SU(2) × SU(2) × U(1). We show that t...
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| Format: | Article |
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SpringerOpen
2025-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP02(2025)205 |
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| author | Hanno Bertle Elli Pomoni Xinyu Zhang Konstantinos Zoubos |
| author_facet | Hanno Bertle Elli Pomoni Xinyu Zhang Konstantinos Zoubos |
| author_sort | Hanno Bertle |
| collection | DOAJ |
| description | Abstract We study the global symmetries of the ℤ 2-orbifold of N $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory and its marginal deformations. The process of orbifolding to obtain an N $$ \mathcal{N} $$ = 2 theory would appear to break the SU(4) R-symmetry down to SU(2) × SU(2) × U(1). We show that the broken generators can be recovered by moving beyond the Lie algebraic setting to that of a Lie algebroid. This remains true when marginally deforming away from the orbifold point by allowing the couplings of the SU(N) × SU(N) gauge groups to vary independently. The information about the marginal deformation is captured by a Drinfeld-type twist of this SU(4) Lie algebroid. The twist is read off from the F- and D- terms, and thus directly from the Lagrangian. Even though at the orbifold point the algebraic structure is associative, it becomes non-associative after the marginal deformation. We explicitly check that the planar Lagrangian of the theory is invariant under this twisted version of the SU(4) algebroid and we discuss implications of this hidden symmetry for the spectrum of the N $$ \mathcal{N} $$ = 2 theory. |
| format | Article |
| id | doaj-art-82f7dae3eec64b91af5cabe2f72ec7f4 |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-82f7dae3eec64b91af5cabe2f72ec7f42025-08-20T03:08:02ZengSpringerOpenJournal of High Energy Physics1029-84792025-02-012025217110.1007/JHEP02(2025)205Hidden symmetries of 4D N $$ \mathcal{N} $$ = 2 gauge theoriesHanno Bertle0Elli Pomoni1Xinyu Zhang2Konstantinos Zoubos3II. Institut für Theoretische Physik, Universität HamburgDeutsches Elektronen-Synchrotron DESYZhejiang Institute of Modern Physics, School of Physics, Zhejiang UniversityDepartment of Physics, University of PretoriaAbstract We study the global symmetries of the ℤ 2-orbifold of N $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory and its marginal deformations. The process of orbifolding to obtain an N $$ \mathcal{N} $$ = 2 theory would appear to break the SU(4) R-symmetry down to SU(2) × SU(2) × U(1). We show that the broken generators can be recovered by moving beyond the Lie algebraic setting to that of a Lie algebroid. This remains true when marginally deforming away from the orbifold point by allowing the couplings of the SU(N) × SU(N) gauge groups to vary independently. The information about the marginal deformation is captured by a Drinfeld-type twist of this SU(4) Lie algebroid. The twist is read off from the F- and D- terms, and thus directly from the Lagrangian. Even though at the orbifold point the algebraic structure is associative, it becomes non-associative after the marginal deformation. We explicitly check that the planar Lagrangian of the theory is invariant under this twisted version of the SU(4) algebroid and we discuss implications of this hidden symmetry for the spectrum of the N $$ \mathcal{N} $$ = 2 theory.https://doi.org/10.1007/JHEP02(2025)205Global SymmetriesQuantum GroupsSupersymmetric Gauge Theory |
| spellingShingle | Hanno Bertle Elli Pomoni Xinyu Zhang Konstantinos Zoubos Hidden symmetries of 4D N $$ \mathcal{N} $$ = 2 gauge theories Journal of High Energy Physics Global Symmetries Quantum Groups Supersymmetric Gauge Theory |
| title | Hidden symmetries of 4D N $$ \mathcal{N} $$ = 2 gauge theories |
| title_full | Hidden symmetries of 4D N $$ \mathcal{N} $$ = 2 gauge theories |
| title_fullStr | Hidden symmetries of 4D N $$ \mathcal{N} $$ = 2 gauge theories |
| title_full_unstemmed | Hidden symmetries of 4D N $$ \mathcal{N} $$ = 2 gauge theories |
| title_short | Hidden symmetries of 4D N $$ \mathcal{N} $$ = 2 gauge theories |
| title_sort | hidden symmetries of 4d n mathcal n 2 gauge theories |
| topic | Global Symmetries Quantum Groups Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP02(2025)205 |
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