Generalized soldering of $\pm 2$ helicity states in $D=2+1$

Understand

The direct sum of a couple of Maxwell-Chern-Simons (MCS) gauge theories of opposite helicities $\pm 1$ does not lead to a Proca theory in $D=2+1$, although both theories share the same spectrum.

• However, it is known that by adding an interference term between both helicities we can join the complementary pieces together and obtain the physically expected result.
• A generalized soldering procedure can be defined to generate the missing interference term.
• Here we show that the same procedure can be applied to join together $\pm 2$ helicity states in a full off-shell manner.