Quantum exact non-abelian vortices in non-relativistic theories

摘要: Non-Abelian vortices arise when a non-Abelian global symmetry is exact in the ground state but spontaneously broken vicinity of their cores. In this case, there appear (non-Abelian) Nambu-Goldstone (NG) modes confined and propagating along vortex. relativistic theories, Coleman-Mermin-Wagner theorem forbids existence spontaneous breaking, or long-range order, 1+1 dimensions: quantum corrections restore vortex NG acquire mass gap. We show that non-relativistic theories with quadratic dispersion relation on can remain gapless at level. provide concrete experimentally realizable example three-component Bose-Einstein condensate U(1) × U(2) symmetry. first show, classical level, S 3 ≃ 1 ⋉ 2 (S fibered over 2) associated to breaking → vortices, where correspond type I II modes, respectively. then by using Bethe ansatz technique, restored, while SU(2) symmery remains non-pertubatively Accordingly, mode turns into c = conformal field theory, Tomonaga-Luttinger liquid, gapless, describing ferromagnetic liquid. This allows be genuinely