Covariant action for M5 brane in nonrelativistic M-theory

We construct the nonrelativistic covariant world-volume action for a single M5 brane of $D=11$ supergravity in M-theory. The corresponding non-Lorentzian (NL) background possesses a codimension three foliation and is identified as the Membrane Newton-Cartan manifold in the presence of background fluxes that are suitably expanded in $1\mathrm{/}{c}^2$ expansion. We also expand the associated world-volume fields in $1\mathrm{/}{c}^2$ expansion. The above procedure eventually results into a well defined world-volume action that is coupled to Membrane Newton-Cartan background.