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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2411.11612 |
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| _version_ | 1866916486273040384 |
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| author | Bertle, Hanno Pomoni, Elli Zhang, Xinyu Zoubos, Konstantinos |
| author_facet | Bertle, Hanno Pomoni, Elli Zhang, Xinyu Zoubos, Konstantinos |
| contents | We study the global symmetries of the $\mathbb{Z}_2$-orbifold of N=4 Super-Yang-Mills theory and its marginal deformations. The process of orbifolding to obtain an N=2 theory would appear to break the $\mathrm{SU}(4)$ R-symmetry down to $\mathrm{SU}(2)\times \mathrm{SU}(2)\times \mathrm{U}(1)$. 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 $ \mathrm{SU}(N)\times \mathrm{SU}(N)$ gauge groups to vary independently. The information about the marginal deformation is captured by a Drinfeld-type twist of this $\mathrm{SU}(4)$ 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 $\mathrm{SU}(4)$ algebroid and we discuss implications of this hidden symmetry for the spectrum of the N=2 theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hidden Symmetries of 4D N=2 Gauge Theories Bertle, Hanno Pomoni, Elli Zhang, Xinyu Zoubos, Konstantinos High Energy Physics - Theory We study the global symmetries of the $\mathbb{Z}_2$-orbifold of N=4 Super-Yang-Mills theory and its marginal deformations. The process of orbifolding to obtain an N=2 theory would appear to break the $\mathrm{SU}(4)$ R-symmetry down to $\mathrm{SU}(2)\times \mathrm{SU}(2)\times \mathrm{U}(1)$. 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 $ \mathrm{SU}(N)\times \mathrm{SU}(N)$ gauge groups to vary independently. The information about the marginal deformation is captured by a Drinfeld-type twist of this $\mathrm{SU}(4)$ 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 $\mathrm{SU}(4)$ algebroid and we discuss implications of this hidden symmetry for the spectrum of the N=2 theory. |
| title | Hidden Symmetries of 4D N=2 Gauge Theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.11612 |