Symmetry extension by condensation defects in five-dimensional gauge theories
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912915804651520 |
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| author | Bertolini, Matteo Di Pietro, Lorenzo Lanza, Stefano C. Niro, Pierluigi Santaniello, Antonio |
| author_facet | Bertolini, Matteo Di Pietro, Lorenzo Lanza, Stefano C. Niro, Pierluigi Santaniello, Antonio |
| contents | We investigate the symmetry structure of five-dimensional Yang-Mills theories with $\mathfrak{su}(N)$ gauge algebra. These theories feature intertwined 0-, 1-, and 2-form symmetries, depending on the global variant one is considering. In the $SU(N)$ theory, there is a mixed 't Hooft anomaly between the instantonic 0-form symmetry and the electric 1-form symmetry. We show that in the $PSU(N)$ theory this translates into a $\mathbb{Z}_N$ extension of the instantonic symmetry, generated by an invertible condensation defect of the magnetic 2-form symmetry. We identify the charged configurations as linked 't Hooft surfaces, while pointlike instanton operators remain insensitive to the extension. We generalize our analysis to the $SU(N)/\mathbb{Z}_k$ global form and show that similar results hold, embedded now in a 3-group structure for generic $k$. We then apply our findings to $SO(3)$ supersymmetric Yang-Mills theory. We determine the global form of the enhanced instantonic symmetry of its superconformal UV completion, showing that it arises through a similar symmetry extension mechanism from the parent $E_1$ theory, which is the UV completion of $SU(2)$ supersymmetric Yang-Mills theory. Finally, we recast our results in the language of the symmetry topological field theory. As a warm-up, we also analyze Maxwell theory, highlighting analogous features involving continuous symmetries and composite currents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry extension by condensation defects in five-dimensional gauge theories Bertolini, Matteo Di Pietro, Lorenzo Lanza, Stefano C. Niro, Pierluigi Santaniello, Antonio High Energy Physics - Theory We investigate the symmetry structure of five-dimensional Yang-Mills theories with $\mathfrak{su}(N)$ gauge algebra. These theories feature intertwined 0-, 1-, and 2-form symmetries, depending on the global variant one is considering. In the $SU(N)$ theory, there is a mixed 't Hooft anomaly between the instantonic 0-form symmetry and the electric 1-form symmetry. We show that in the $PSU(N)$ theory this translates into a $\mathbb{Z}_N$ extension of the instantonic symmetry, generated by an invertible condensation defect of the magnetic 2-form symmetry. We identify the charged configurations as linked 't Hooft surfaces, while pointlike instanton operators remain insensitive to the extension. We generalize our analysis to the $SU(N)/\mathbb{Z}_k$ global form and show that similar results hold, embedded now in a 3-group structure for generic $k$. We then apply our findings to $SO(3)$ supersymmetric Yang-Mills theory. We determine the global form of the enhanced instantonic symmetry of its superconformal UV completion, showing that it arises through a similar symmetry extension mechanism from the parent $E_1$ theory, which is the UV completion of $SU(2)$ supersymmetric Yang-Mills theory. Finally, we recast our results in the language of the symmetry topological field theory. As a warm-up, we also analyze Maxwell theory, highlighting analogous features involving continuous symmetries and composite currents. |
| title | Symmetry extension by condensation defects in five-dimensional gauge theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.16165 |