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arXiv · 2512.13934

One constant to rule them all

Aleksei Bykov·Ekaterina Sysoeva
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Abstract

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.

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Aleksei Bykov, Ekaterina Sysoeva. 2025-12-15. One constant to rule them all. https://arxiv.org/abs/2512.13934

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