Boundary dynamics of Maxwell-invariant three-dimensional Chern-Simons gravity

We construct a two-dimensional dual field theory induced at the boundary of three-dimensional Chern-Simons gravity invariant under the Maxwell algebra. The resulting action takes the form of a Maxwellian extension of the flat Liouville theory known from the analysis of asymptotically flat three-dimensional gravity. This boundary theory is derived by reducing the bulk gravitational action to a Maxwell-invariant chiral Wess-Zumino-Witten model and imposing boundary conditions compatible with asymptotically flat geometries. Alternatively, we obtain the same theory as the geometric action on coadjoint orbits of the Maxwell extension of the BMS$_3$ group. Finally, we show how the boundary actions corresponding to both Poincar\'e and Maxwell invariance emerge from a Carrollian expansion of the boundary theory dual to AdS$_3$ Chern-Simons gravity.