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Peer-reviewedCC BY 4.0Journal of High Energy Physics

One constant to rule them all

  • Aleksei Bykov1
  • Ekaterina Sysoeva1
  1. 1Dipartimento di Fisica, Università di Torino, and I.N.F.N. — sezione di Torino
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Abstract

We study the coupling matrix of 𝒩 = 2 SU(N) gauge theories with 2N fundamental hypermultiplets in the special vacuum, where a residual ℤN symmetry restores nontrivial modular structure. Using symmetry and dimensional arguments, we construct its general form and identify ⌊N/2⌋ 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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Cite

BibTeXRIS
BibTeX
@article{bykov2026constant,
  title = {{One constant to rule them all}},
  author = {Aleksei Bykov and Ekaterina Sysoeva},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = nov,
  doi = {10.1007/jhep11(2026)019},
  url = {https://link.springer.com/article/10.1007/JHEP11(2026)019},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - One constant to rule them all
AU  - Aleksei Bykov
AU  - Ekaterina Sysoeva
PY  - 2026
DA  - 2026/11/04
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep11(2026)019
UR  - https://link.springer.com/article/10.1007/JHEP11(2026)019
AB  - We study the coupling matrix of 𝒩 = 2 SU(N) gauge theories with 2N fundamental hypermultiplets in the special vacuum, where a residual ℤN symmetry restores nontrivial modular structure. Using symmetry and dimensional arguments, we construct its general form and identify ⌊N/2⌋ 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.
SN  - 1029-8479
ER  -