Supertranslation Goldstone and de Sitter Tachyons

TL;DR

This paper explores the connection between supertranslation Goldstone modes and de Sitter tachyons through representation theory, revealing a shared structure in certain symmetry representations and discussing unitarity properties.

Contribution

It identifies a common representation-theoretic framework for supertranslation Goldstone modes and de Sitter tachyons, highlighting their structural similarities and unitarity conditions.

Findings

Supertranslation Goldstone modes and de Sitter tachyons share the same SL(2,C) representation.

A unitary representation exists for these theories when considering polynomials.

Representation-theoretical analysis clarifies the structure and properties of these fields.

Abstract

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.