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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Global forms of 𝒩 = 4 theories and non-minimal Seiberg-Witten solutions

  • Robert Moscrop1,2
  1. 1Harvard University
  2. 2Uppsala University
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Abstract

A bstract : To each four dimensional 𝒩 N β‰₯ 2 supersymmetric quantum field theory, one can associate an algebraic completely integrable (ACI) system that encodes the low energy dynamics of theory. In this paper we explicitly derive the appropriate ACI systems for the global forms of 𝒩 N = 4 super Yang-Mills (sYM) using isogenies of polarised abelian varieties. In doing so, we relate the complex moduli of the resulting varieties to the exactly marginal coupling of the theory, thus allowing us to probe the S -duality groups of the global forms. Finally, we comment on whether the resulting varieties are the Jacobians of a minimal genus Riemann surface, coming to the conclusion that many global forms of 𝒩 N = 4 sYM do not admit a minimal genus Seiberg-Witten curve that correctly reproduces the global form.

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Cite

BibTeXRIS
BibTeX
@article{moscrop2026global,
  title = {{Global forms of $$ \mathcalN $$ = 4 theories and non-minimal Seiberg-Witten solutions}},
  author = {Robert Moscrop},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)096},
  url = {https://link.springer.com/10.1007/JHEP10(2026)096},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Global forms of 𝒩 = 4 theories and non-minimal Seiberg-Witten solutions
AU  - Robert Moscrop
PY  - 2026
DA  - 2026/10/08
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)096
UR  - https://link.springer.com/10.1007/JHEP10(2026)096
AB  - A bstract : To each four dimensional 𝒩 N β‰₯ 2 supersymmetric quantum field theory, one can associate an algebraic completely integrable (ACI) system that encodes the low energy dynamics of theory. In this paper we explicitly derive the appropriate ACI systems for the global forms of 𝒩 N = 4 super Yang-Mills (sYM) using isogenies of polarised abelian varieties. In doing so, we relate the complex moduli of the resulting varieties to the exactly marginal coupling of the theory, thus allowing us to probe the S -duality groups of the global forms. Finally, we comment on whether the resulting varieties are the Jacobians of a minimal genus Riemann surface, coming to the conclusion that many global forms of 𝒩 N = 4 sYM do not admit a minimal genus Seiberg-Witten curve that correctly reproduces the global form.
SN  - 1029-8479
ER  -