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| Auteurs principaux: | , |
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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2512.13934 |
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| _version_ | 1866910220246056960 |
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| author | Bykov, Aleksei Sysoeva, Ekaterina |
| author_facet | Bykov, Aleksei Sysoeva, Ekaterina |
| contents | We study the coupling matrix of $\mathcal{N}=2$ $SU(N)$ gauge theories with $2N$ fundamental hypermultiplets in the special vacuum, where a residual $\mathbb{Z}_N$ symmetry restores nontrivial modular structure. Using symmetry and dimensional arguments, we construct its general form and identify $\lfloor N/2 \rfloor$ coupling constants in their most natural basis. We show that in the massless theory these couplings transform independently under $S$-duality and that the bare coupling is a modular function of any of them. One coupling constant, however, plays a distinguished role, emerging in the asymptotic regime and in instanton recursion relation. In the massive case, this structure is deformed but the distinguished coupling retains its privileged role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13934 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One constant to rule them all Bykov, Aleksei Sysoeva, Ekaterina High Energy Physics - Theory We study the coupling matrix of $\mathcal{N}=2$ $SU(N)$ gauge theories with $2N$ fundamental hypermultiplets in the special vacuum, where a residual $\mathbb{Z}_N$ symmetry restores nontrivial modular structure. Using symmetry and dimensional arguments, we construct its general form and identify $\lfloor N/2 \rfloor$ coupling constants in their most natural basis. We show that in the massless theory these couplings transform independently under $S$-duality and that the bare coupling is a modular function of any of them. One coupling constant, however, plays a distinguished role, emerging in the asymptotic regime and in instanton recursion relation. In the massive case, this structure is deformed but the distinguished coupling retains its privileged role. |
| title | One constant to rule them all |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.13934 |