Speaker
Dmitri Bykov
(S)
Description
We solve the classical and quantum problems for the 1D sigma model with target space the flag manifold U(3)/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 U(n) case.
This talk is based on a series of joint papers with A. Kuzovchikov and V. Krivorol:
- D. Bykov and A. Kuzovchikov. “The classical and quantum particle on a flag manifold”. arXiv:2404.15900 [hep-th]
- D. Bykov, V. Krivorol and A. Kuzovchikov. “Oscillator Calculus on Coadjoint Orbits and Index Theorems”. arXiv:2412.21024 [hep-th]
- D. Bykov and A. Kuzovchikov. “Sigma models from Gaudin spin chains”. arXiv:2508.20889 [hep-th]
Author
Dmitri Bykov
(S)
