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

A bstract 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. Based on the BMS 3 /Carroll-CFT duality, we show how the boundary actions corresponding to both Poincaré and Maxwell invariance emerge from a Carrollian expansion of the boundary theory dual to AdS 3 Chern-Simons gravity. Finally, we discuss how the Maxwellian boundary dual theory can be obtained as the geometric action on coadjoint orbits of the Maxwell extension of the BMS 3 group.