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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.21071 |
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| _version_ | 1866918352159506432 |
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| author | Comi, Riccardo Garavaglia, Sebastiano Giacomelli, Simone Pasquetti, Sara Singh, Palash |
| author_facet | Comi, Riccardo Garavaglia, Sebastiano Giacomelli, Simone Pasquetti, Sara Singh, Palash |
| contents | We study weakly-coupled descriptions/channel decompositions of the 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ of type $\mathfrak{su}(N)$, from the perspective of the 3d $\mathcal{N}=4$ mirror duals of their circle compactifications. This is a delicate problem when the channel decomposition produces pathological, or bad, 4d configurations that correspond to spheres with non-maximal punctures. The star-shaped quivers, describing the 3d mirrors associated with such bad 4d configurations, are bad 3d $\mathcal{N}=4$ theories. Leveraging recent results regarding 3d bad theories, we identify a new and interesting family of bad theories, which we coin \textit{broken} theories, that naturally arise in this context. Using these broken theories, we develop a systematic and analytic method that determines the generically non-Lagrangian matter sectors and the weakly-coupled gauge groups in such channel decompositions. We understand these weakly-coupled descriptions as emerging dynamically via Higgs mechanisms triggered by operators acquiring vacuum expectation values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Breaking bad theories of class $\mathcal S$ Comi, Riccardo Garavaglia, Sebastiano Giacomelli, Simone Pasquetti, Sara Singh, Palash High Energy Physics - Theory We study weakly-coupled descriptions/channel decompositions of the 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ of type $\mathfrak{su}(N)$, from the perspective of the 3d $\mathcal{N}=4$ mirror duals of their circle compactifications. This is a delicate problem when the channel decomposition produces pathological, or bad, 4d configurations that correspond to spheres with non-maximal punctures. The star-shaped quivers, describing the 3d mirrors associated with such bad 4d configurations, are bad 3d $\mathcal{N}=4$ theories. Leveraging recent results regarding 3d bad theories, we identify a new and interesting family of bad theories, which we coin \textit{broken} theories, that naturally arise in this context. Using these broken theories, we develop a systematic and analytic method that determines the generically non-Lagrangian matter sectors and the weakly-coupled gauge groups in such channel decompositions. We understand these weakly-coupled descriptions as emerging dynamically via Higgs mechanisms triggered by operators acquiring vacuum expectation values. |
| title | Breaking bad theories of class $\mathcal S$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.21071 |