Supersymmetric dS/CFT

TL;DR

This work proposes a supersymmetric realization of dS/CFT by linking ${\cal N}=2$ Euclidean vector models with reversed spin-statistics to ${\cal N}=2$ Vasiliev higher-spin theories in de Sitter space. By constructing the free ${U(-N)}$ theory and its SUSY deformations, the authors show that the partition function can define a well-behaved Hartle-Hawking wave function $\Psi_{HH}$ for a minisuperspace of asymptotically de Sitter geometries, with a global maximum at undeformed dS and suppressed contributions from strong deformations. They derive explicit results for scalar deformations and SUSY-preserving squashed geometries, demonstrating that the SUSY structure removes ghost-like instabilities and yields normalizable wave functions in the HS dS context. The paper further speculates on a broader triality with exotic string theories, suggesting a tensionless limit of such theories could underlie the dS HS duals, thereby offering a framework for holographic cosmology in de Sitter space and guiding future explorations of interacting SUSY HS dS duals and localization techniques.

Abstract

We put forward new explicit realisations of dS/CFT that relate ${\cal N}=2$ supersymmetric Euclidean vector models with reversed spin-statistics in three dimensions to specific supersymmetric Vasiliev theories in four-dimensional de Sitter space. The partition function of the free supersymmetric vector model deformed by a range of low spin deformations that preserve supersymmetry appears to specify a well-defined wave function with asymptotic de Sitter boundary conditions in the bulk. In particular we find the wave function is globally peaked at undeformed de Sitter space, with a low amplitude for strong deformations. This suggests that supersymmetric de Sitter space is stable in higher-spin gravity and in particular free from ghosts. We speculate this is a limiting case of the de Sitter realizations in exotic string theories.

Figures (2)

• Figure 1: The response of $Z Z^*$ to various mass deformations for two chiral multiplets with reversed spin-statistics. We conjecture this corresponds to the Hartle-Hawking wave function in a homogeneous isotropic minisuperspace model in HS gravity. Left: Both multiplets are in the same representation of the gauge multiplets inducing the mass deformation \ref{['massdeform']} with parameter $m$. Right: the two multiplets are in opposite representations; one has mass parameter $m$ and the other $-m$ under \ref{['massdeform']}.
• Figure 2: The holographic Hartle-Hawking wave function in higher-spin gravity in the one-dimensional minisuperspace of anisotropic but homogeneous deformations of de Sitter coupled to a gauge field, parameterized by $v$, for a single multiplet.