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Flassig, Daniel; Franca, Andre and Pritzel, Alexander (2016): Large-N ground state of the Lieb-Liniger model and Yang-Mills theory on a two-sphere. In: Physical Review A, Vol. 93, No. 1, 13627

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We derive the large-particle-number limit of the Bethe equations for the ground state of the attractive one-dimensional Bose gas (Lieb-Liniger model) on a ring and solve it for arbitrary coupling. We show that the ground state of this system can be mapped to the large-N saddle point of Euclidean Yang-Mills theory on a two-sphere with a U(N) gauge group, and the phase transition that interpolates between the homogeneous and solitonic regime is dual to the Douglas-Kazakov confinement-deconfinement phase transition.

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