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PreprintCC BY 4.0arXiv

Doubly-periodic instanton via the ADHM method and the self-dual monopole-center vortex chain

  • Yui Hayashi
  • Yuya Tanizaki
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Abstract

Calorons, i.e., instantons on ℝ3× S1, with nontrivial asymptotic holonomy decompose into N fundamental monopole constituents. This suggests that a doubly-periodic Yang--Mills instanton on ℝ2× T2 may admit a description in terms of a periodic array of monopole constituents. Starting from the Atiyah--Drinfeld--Hitchin--Manin (ADHM) construction, we derive the $2$d Abelian Hitchin system with impurities as a dual description of the doubly-periodic instanton. We then give a prescription for reconstructing the instanton from the Green's function of this system, assuming a scaling ansatz for the ultraviolet divergences induced by the delta-function impurities. In the far-field limit with strongly anisotropic torus periods, we extend the analysis of Bruckmann and van Baal for multi-calorons and identify an alternating chain of BPS and Kaluza--Klein (KK) monopole constituents: The monopole-center vortex chain arises from the non-Abelian self-dual field especially when an 't Hooft twist cuts the torus into the 1/N fragment.

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Cite

BibTeXRIS
BibTeX
@misc{hayashi2026doublyperiodic,
  title = {{Doubly-periodic instanton via the ADHM method and the self-dual monopole-center vortex chain}},
  author = {Yui Hayashi and Yuya Tanizaki},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00639},
  eprint = {2611.00639},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00639},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Doubly-periodic instanton via the ADHM method and the self-dual monopole-center vortex chain
AU  - Yui Hayashi
AU  - Yuya Tanizaki
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00639
UR  - https://arxiv.org/abs/2611.00639
AB  - Calorons, i.e., instantons on ℝ^3× S^1, with nontrivial asymptotic holonomy decompose into N fundamental monopole constituents. This suggests that a doubly-periodic Yang--Mills instanton on ℝ^2× T^2 may admit a description in terms of a periodic array of monopole constituents. Starting from the Atiyah--Drinfeld--Hitchin--Manin (ADHM) construction, we derive the $2$d Abelian Hitchin system with impurities as a dual description of the doubly-periodic instanton. We then give a prescription for reconstructing the instanton from the Green's function of this system, assuming a scaling ansatz for the ultraviolet divergences induced by the delta-function impurities. In the far-field limit with strongly anisotropic torus periods, we extend the analysis of Bruckmann and van Baal for multi-calorons and identify an alternating chain of BPS and Kaluza--Klein (KK) monopole constituents: The monopole-center vortex chain arises from the non-Abelian self-dual field especially when an 't Hooft twist cuts the torus into the 1/N fragment.
ER  -