Sigma models from Gaudin spin chains

Dmitri Bykov; Andrew Kuzovchikov

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arXiv · 2508.20889

Sigma models from Gaudin spin chains

Dmitri Bykov·Andrew Kuzovchikov

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Abstract

We solve the classical and quantum problems for the 1D sigma model with target space the flag manifold $\mathrm{U}(3)\over \mathrm{U}(1)^3$, equipped with the most general invariant metric. In particular, we explicitly describe all geodesics in terms of elliptic functions and demonstrate that the spectrum of the Laplace-Beltrami operator may be found by solving polynomial (Bethe) equations. The main technical tool that we use is a mapping between the sigma model and a Gaudin model, which is also shown to hold in the $\mathrm{U}(n)$ case.

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Dmitri Bykov, Andrew Kuzovchikov. 2025-08-28. Sigma models from Gaudin spin chains. https://arxiv.org/abs/2508.20889

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