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  • Letter
  • Open Access

Integrable systems for generalized toric polygons and Higgsed 5D N=1 theories

Minsung Kho*

Kimyeong Lee†

Norton Lee‡

Rak-Kyeong Seong§

  • *Contact author: minsung@unist.ac.kr
  • †Contact author: klee@bimsa.cn
  • ‡Contact author: norton.lee@ibs.re.kr
  • §Contact author: seong@unist.ac.kr
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Phys. Rev. D 114, L081906 – Published 21 October, 2026

DOI: https://doi.org/10.1103/p4tc-mhkg

Abstract

The interplay between toric Calabi-Yau 3-folds, cluster integrable systems, and 5-dimensional quantum field theories has proved fruitful. We extend this framework to generalized toric polygons (GTPs) and show that their integrable systems arise from refined birational transformations of known cluster integrable systems acting on the Casimirs and Hamiltonians as well as the Poisson structure and spectral curves. We argue that these transformations are realized as Hanany-Witten transitions producing (p,q) 5-brane webs dual to GTPs. We show that the resulting 5D N=1 theory is obtained by Higgsing a higher-rank theory whose associated toric Calabi-Yau has a toric diagram of the same shape as the GTP.

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Phys. Rev. D 114, L081906– Published 21 October, 2026
  • Received 29 March 2026
  • Accepted 1 October 2026
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