Massive Gravity: A Primer

We show that the recently constructed 3D higher-derivative “New Massive Gravity theory” is the result of a general procedure that allows one to construct, in the free case, higher-derivative gauge theories for a wide class of “spins” in diverse dimensions. We specify the criterium that the “spin” and dimension need to satisfy in order for the construction to apply. To clarify the general procedure we present examples of higher-derivative gauge theories for the special cases of spin 1 in D=3, 5 and 7 dimensions. We next apply the procedure to spin 2 in D=3 dimensions and show how the New Massive Gravity and Topological Massive Gravity theories are constructed. Both theories allow interactions. We indicate how and under which conditions the 3D New Massive Gravity theory can be extended to D=4 dimensions and the 3D Topological Massive Gravity theory can be extended to D=7 dimensions. We discuss the issue of interactions of these two theories.