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

TL;DR

This paper introduces a novel unitary supersymmetric quantum field theory on fixed de Sitter spacetime, featuring chiral graviton and gravitino fields, overcoming previous obstacles by utilizing conformal algebra symmetries.

Contribution

It presents the first unitary supersymmetric theory on de Sitter space with a symmetry algebra closing on conformal algebra instead of de Sitter algebra.

Findings

The theory is consistent and unitary on $dS_4$.

Supersymmetry transformations close on $so(4,2)$ conformal algebra.

Unconventional conformal-like transformations realize the symmetry.

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.