Large-N ground state of the Lieb-Liniger model and Yang-Mills theory on a two-sphere

Abstract

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 confimenent-deconfinement phase transition.

11 pages, 3 figures; added references

References in corpus (6)

• Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
• Correlation functions of the one-dimensional attractive Bose gas
• Black Holes and Quantumness on Macroscopic Scales
• Metastable criticality and the super Tonks-Girardeau gas
• Nambu-Goldstone Effective Theory of Information at Quantum Criticality
• Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz

Cited by in corpus (10)

• Reversible quantum information spreading in many-body systems near criticality
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Quench action and large deviations: work statistics in the one-dimensional Bose gas
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• $\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas
• The Timescales of Quantum Breaking
• Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz
• Stückelberg Formulation of Holography
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
• An exact solution to asymptotic Bethe equation