Unitary SUSY for the chiral graviton and chiral gravitino in de Sitter spacetime

TL;DR

The paper tackles the long-standing issue of unitary supersymmetry on fixed $dS_4$ by constructing a free, unitary QFT consisting of a chiral graviton and a chiral gravitino. The key idea is to extend the symmetry from $so(4,1)$ to $so(4,2)$ via unconventional conformal-like transformations, so that the SUSY algebra closes on $so(4,2)igoplus u(1)$ rather than on $so(4,1)$, thereby enabling unitarity. The chiral fields are complex and subject to anti-self-duality constraints (F^- for the gravitino and U^- for the graviton), with mode expansions that realize $so(4,2)$ UIRs and respect conformal-like symmetry. Rigorous unitarity is demonstrated by constructing appropriate inner products, verifying the closure of the SUSY algebra on $so(4,2)igoplus u(1)$, and showing positivity of the (anti)commutators of the supercharges; the work also discusses the possibility of a non-linear, local SUSY completion as an open question. Overall, the results establish a concrete framework for unitary rigid SUSY on $dS_4$, highlighting the role of enhanced conformal-like symmetries in circumventing prior no-go results.

Abstract

It is commonly believed that a unitary supersymmetric quantum field theory (QFT) involving graviton and gravitino fields on fixed 4-dimensional de Sitter spacetime ($dS_4$) cannot exist due to known challenges associated with supersymmetry (SUSY) on spaces with positive cosmological constant. In this talk, we contradict this expectation by presenting a new unitary supersymmetric QFT on fixed $dS_4$ : the free supersymmetric theory of the chiral graviton and chiral gravitino fields. The theory overcomes the known obstacles to unitary global SUSY on de Sitter because the commutator between two SUSY transformations closes on the conformal algebra $so(4,2)$ rather than the de Sitter algebra $so(4,1)$. Crucially, the $so(4,2)$ symmetry is realised through unconventional conformal-like transformations. Based on arxiv:2503.04515.