Supertranslation Goldstone and de Sitter Tachyons

Supertranslation Goldstone lies in certain “exceptional series” representations of $SL(2,\mathbb{C})$. Interestingly, $m^2=-3$ scalar tachyon in three dimensional de Sitter space also lies in the same representation. In this note, we analyze these theories, focusing on representation-theoretical aspects, and emphasize that “modulo certain polynomials”, there is a unitary representation of the corresponding symmetry group.