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arXiv · 2610.31672

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 $\mathcal{N}=2$ 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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G. Bonelli, S. Lacroix, T. Pedroni, A. Tanzini. 2026-10-22. Ricci flow of Integrable Sigma Models, Hitchin Systems and Quantum Seiberg-Witten theory. https://arxiv.org/abs/2610.31672

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