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

TL;DR

This paper analyzes the large-N limit of the Lieb-Liniger model's ground state and reveals its connection to Yang-Mills theory on a two-sphere, uncovering a phase transition analogous to confinement-deconfinement.

Contribution

It establishes a novel mapping between the ground state of the attractive Bose gas and the large-N saddle point of Euclidean Yang-Mills theory on a sphere, including phase transition insights.

Findings

Derived the large-N limit of Bethe equations for the Lieb-Liniger model.

Mapped the ground state to the large-N saddle point of Yang-Mills theory.

Identified a phase transition analogous to the Douglas-Kazakov transition.

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.