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Motivated by the spin current problem in chiral helimagnet, we rigorouslyelucidated the hidden Galilean invariance in the chiral XY model under themagnetic field. The Lie group analysis is applied to the differential equationsof the continuum theory of the chiral helimagnet with the parity-violatingDzyaloshinskii-Morya coupling under a transversal magnetic field. Lie pointsymmetries and the invariant solutions under these symmetries are found. Theypresent sliding solutions that come up as a consequence of breaking of bothspin rotational symmetry by the external magnetic field and a parity violationdue to the Dzyaloshinskii-Morya interaction. We found that variationalsymmetries are related with translations in space and time, the correspondingenergy and momentum conservation laws are derived. We therefore succeeded injustifying the existence of the transport spin current in chiral helimagnet.

Hidden Galilean symmetry, conservation laws and emergence of spin current in the soliton sector of chiral helimagnet