Supersymmetric dS/CFT (1709.06024v2)

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.

• The paper introduces a supersymmetric dS/CFT duality by pairing 3D Euclidean vector models with 4D de Sitter higher-spin theories.
• It analyzes deformations of the partition function to show that the wave function peaks at undeformed dS space, indicating stability.
• The findings suggest supersymmetry may stabilize de Sitter higher-spin theories and potentially link them to exotic string theory scenarios.

Overview of "Supersymmetric dS/CFT"

The paper "Supersymmetric dS/CFT" investigates a supersymmetric generalization of the dS/CFT duality, positing an explicit correspondence between three-dimensional supersymmetric Euclidean vector models and specific four-dimensional de Sitter (dS) higher-spin theories. The authors present a compelling framework that integrates supersymmetry into the higher-spin holographic paradigm, thereby extending the conceptual landscape of holographic dualities into de Sitter space. This paper contributes to our understanding of both the formal aspects of holographic dualities and their broader implications in theoretical physics, particularly in considering de Sitter space from a holographic perspective.

Summary of Key Contributions

1. Supersymmetric Extension of dS/CFT: The authors introduce a novel realization of the dS/CFT correspondence, using $\mathcal{N}=2$ supersymmetric Euclidean vector models in three dimensions, which feature reversed spin-statistics, as the CFT duals. In the bulk, these models are conjectured to correspond to specific supersymmetric higher-spin theories in de Sitter space. This extension addresses the profound challenge of incorporating supersymmetry into the dS/CFT framework, which is non-trivial due to the complexities associated with de Sitter (dS) spacetimes.
2. Deformations and Wave Function Analysis: The research analyzes the partition function of the supersymmetric vector model deformed by various low-spin supersymmetric-preserving currents. The models are examined for their role in defining a wave function for the universe within a minisuperspace setting, under de Sitter boundary conditions. Notably, the wave function peaks at undeformed de Sitter space, suggesting inherent stability, and shows a reduced amplitude for strong deformations.
3. Theoretical Implications: Supersymmetry is intriguingly postulated to provide a mechanism for stability within higher-spin theories in de Sitter space, despite conventional arguments rejecting unbroken supersymmetry in such spaces due to the absence of a positive conserved energy. The paper hypothesizes that these supersymmetric higher-spin dS theories may potentially link to exotic string theories, indicating a broader context where non-standard moves, including complex boundary configurations, provide a coherent structure devoid of ghosts.
4. Numerical Results: The authors conduct numerical analysis of the partition function under mass and metric deformations, revealing a highly localized maximum around pure de Sitter configurations. This finding aligns with theoretical expectations from holographic principles and points toward a stable region indicative of physical behavior free from significant pathologies.

Implications and Speculations

The research opens various avenues for further investigation. The implications of supersymmetric dS/CFT hint at deeper connections possibly extending to exotic formulations of string theory, suggesting a wider triality or duality setup. This could significantly alter our understanding of quantum gravity and cosmology in the de Sitter space context.

The work also provides groundwork for future studies, particularly in exploring the boundary-bulk relationships in settings with higher supersymmetry and interacting fields beyond free theories. Moreover, the insights on minisuperspace models and their wave functions broaden the discourse on cosmic inflation and stability of de Sitter space, compelling us to reconsider the foundational notions of vacuum stability in quantum gravity.

Overall, this paper stakes a claim on the frontier of theoretical physics, proposing speculative yet plausible interconnections between seemingly disparate realms, fostering a landscape where higher-spin theories, supersymmetry, and holographic principles converge toward a coherent cosmological paradigm.