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PreprintCC BY 4.0arXiv

Ricci flow of Integrable Sigma Models, Hitchin Systems and Quantum Seiberg-Witten theory

  • G. Bonelli
  • S. Lacroix
  • T. Pedroni
  • A. Tanzini
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Abstract

We construct a family of integrable 2d sigma models through 4d Chern-Simons theory and show that their classical point-particle reduction corresponds to a Hitchin system. The integrable Hitchin quantisation then provides a natural candidate Hamiltonian for the one-loop reduced dynamics of the sigma models, which coincides with the Perelman operator in all cases examined. This allows us to study the corresponding spectral problems using 4d 𝒩=2 gauge theory and 2d conformal field theory methods. For the sausage model, we derive exact quantisation conditions and compute exponentially small corrections essential for the agreement with numerical finite-volume results.

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Cite

BibTeXRIS
BibTeX
@misc{bonelli2026ricci,
  title = {{Ricci flow of Integrable Sigma Models, Hitchin Systems and Quantum Seiberg-Witten theory}},
  author = {G. Bonelli and S. Lacroix and T. Pedroni and A. Tanzini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31672},
  eprint = {2610.31672},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31672},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Ricci flow of Integrable Sigma Models, Hitchin Systems and Quantum Seiberg-Witten theory
AU  - G. Bonelli
AU  - S. Lacroix
AU  - T. Pedroni
AU  - A. Tanzini
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31672
UR  - https://arxiv.org/abs/2610.31672
AB  - We construct a family of integrable 2d sigma models through 4d Chern-Simons theory and show that their classical point-particle reduction corresponds to a Hitchin system. The integrable Hitchin quantisation then provides a natural candidate Hamiltonian for the one-loop reduced dynamics of the sigma models, which coincides with the Perelman operator in all cases examined. This allows us to study the corresponding spectral problems using 4d 𝒩=2 gauge theory and 2d conformal field theory methods. For the sausage model, we derive exact quantisation conditions and compute exponentially small corrections essential for the agreement with numerical finite-volume results.
ER  -