Higher Spin Realization of the dS/CFT Correspondence (1108.5735v1)

Abstract: We conjecture that Vasiliev's theory of higher spin gravity in four-dimensional de Sitter space (dS) is holographically dual to a three-dimensional conformal field theory (CFT) living on the spacelike boundary of dS at future timelike infinity. The CFT is the Euclidean Sp(N) vector model with anticommuting scalars. The free CFT flows under a double-trace deformation to an interacting CFT in the IR. We argue that both CFTs are dual to Vasiliev dS gravity but with different future boundary conditions on the bulk scalar field. Our analysis rests heavily on analytic continuations of bulk and boundary correlators in the proposed duality relating the O(N) model with Vasiliev gravity in AdS.

• The paper demonstrates a duality between Vasiliev’s higher spin gravity in de Sitter space and two Sp(N) CFTs, each corresponding to distinct boundary conditions.
• The authors employ analytic continuation techniques to map EAdS correlators to dS4, rigorously validating the transformation of singlet correlators.
• The study highlights implications for non-perturbative quantum gravity and cosmology, addressing pseudo-unitarity in the Sp(N) CFT framework.

Higher Spin Realization of the DS/CFT Correspondence

The paper authored by Dionysios Anninos, Thomas Hartman, and Andrew Strominger at prominent institutes such as Stanford, Princeton, and Harvard, seeks to elucidate a potential duality in the field of quantum gravity. Specifically, the authors conjecture a dS/CFT correspondence that unveils a holographic duality between Vasiliev's higher spin gravity theory in four-dimensional de Sitter space (dS$_4$) and a three-dimensional conformal field theory (CFT) on its future spacelike boundary.

The CFT in question is identified as the Euclidean Sp(N) vector model, characterized by anticommuting scalars. This framework posits a parallel with the established AdS/CFT correspondence, where the conjectured duality is relevant to AdS quantum gravity. However, the move from AdS to dS brings about non-trivial challenges, primarily due to the nature of time and its emergence holographically in the dS context.

Key Arguments and Claims

• Dual CFTs: The paper argues that two distinct Sp(N) CFTs, one free and the other interacting due to a double-trace deformation, relate to Vasiliev dS gravity under different boundary conditions. Free CFTs correspond to Neumann conditions, while interacting CFTs align with Dirichlet boundary conditions, analogous to prior GKPY dualities where similar CFT gravity dualities in AdS spaces were constructed.
• Analytic Continuation: The authors extensively utilize analytic continuation techniques to relate correlators from Vasiliev’s theory in EAdS to those in dS$_4$, leveraging the mathematical similarities while adjusting for differences in boundary conditions introduced by the change in the sign of cosmological constants.
• Pseudo-Unitary Structure: An intriguing aspect of the Sp(N) CFT representation is its inherent non-unitarity due to anticommuting scalars. Nonetheless, a pseudo-unitary structure is identified, which might hold relevance for dS/CFT, permitting meaningful duality despite the unconventional properties in standard unitarity frameworks.

Numerical Results

The paper provides a robust mathematical derivation of singlet correlators, demonstrating their transformation under analytically continued parameters (notably $N \to -N$). The consistency of these transformations with prior O(N) model results in AdS scenarios suggests the viability of the duality and aids in validating Vasiliev's higher-spin gravity model as a candidate for describing dS physics.

Implications

1. Impact on Quantum Gravity: If proven accurate, the dS/CFT correspondence could provide substantial insights into non-perturbative quantum gravity formulations in de Sitter spaces, potentially illuminating paths to resolving cosmological constant issues and bridging quantum mechanics with gravitation.
2. Theoretical Advancements: The conjecture supports theoretical frameworks that leverage higher spin symmetries to explore new territories about universal properties of high-dimensional gravitational theories.
3. Practical Applications: Beyond theory, there exists a possibility for practical implications, such as analyzing cosmic microwave background data in inflationary era models, which may share universal properties delineated by dS/CFT correspondence.

Future Directions

The current model predicates future research extensions that could encompass refining the mathematical underpinnings, establishing more explicit links to empirical observations, and investigating broader applications or alternative higher spin gravity models. Further efforts could also explore potential connections with string theory, despite existing discrepancies noted for analogous AdS solutions.

In conclusion, the paper requires considerable scrutiny and offers a fertile ground for innovative theoretical physics explorations. As such, it provides a provocative yet systematically elaborated framework that promises to foster further advancements within the field of quantum gravity and holography.