Quantum Exact Non-Abelian Vortices in Non-relativistic Theories

Understand

Non-Abelian vortices arise when a non-Abelian global symmetry is exact in the ground state but spontaneously broken in the vicinity of their cores.

• In this case, there appear (non-Abelian) Nambu-Goldstone (NG) modes confined and propagating along the vortex.
• In relativistic theories, the Coleman-Mermin-Wagner theorem forbids the existence of a spontaneous symmetry breaking, or a long-range order, in 1+1 dimensions: quantum corrections restore the symmetry along the vortex and the NG modes acquire a mass gap.
• We show that in non-relativistic theories NG modes with quadratic dispersion relation confined on a vortex can remain gapless at quantum level.