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From 2D Yang-Mills to Calogero-Sutherland via a colored particle
Marcia Tenser, Amilcar R. Queiroz·June 11, 2026
hep-thMathematical PhysicsQuantum Physics
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Abstract
We study Yang-Mills theory coupled to a particle on a cylinder, where gauge invariance and compactness reduce the dynamics to a finite dimensional quantum system. In the Abelian case, this yields a model equivalent to the Landau problem on a torus, with a degenerate ground state structure. We generalize this construction to non-Abelian gauge groups and show that, for SU(N), the system reduces to a one dimensional quantum many body problem with a singular Calogero-Sutherland-type interaction.