Gauged Wess–Zumino–Witten actions for generalized Poincaré algebras

Abstract

If the Chern–Simons theory is the appropriate gauge theory for the gravitational interaction, then these theories must satisfy the correspondence principle, namely they must be related to General Relativity.In this Letter a five-dimensional Chern–Simons action invariant under the generalized Poincaré algebra B5 is constructed and then it is proved that the corresponding gauged Wess–Zumino–Witten term contains the Einstein–Hilbert action. In the same way, we show that a five-dimensional Chern–Simons action, invariant under the Maxwell algebra B4, induces a gauged Wess–Zumino–Witten term that coincides with the four-dimensional topological gravity.