Antipodally symmetric gauge fields and higher-spin gravity in de Sitter space

Abstract: We study gauge fields of arbitrary spin in de Sitter space. These include Yang-Mills fields and gravitons, as well as the higher-spin fields of Vasiliev theory. We focus on antipodally symmetric solutions to the field equations, i.e. ones that live on "elliptic" de Sitter space dS_4/Z_2. For free fields, we find spanning sets of such solutions, including boundary-to-bulk propagators. We find that free solutions on dS_4/Z_2 can only have one of the two types of boundary data at infinity, meaning that the boundary 2-point functions vanish. In Vasiliev theory, this property persists order by order in the interaction, i.e. the boundary n-point functions in dS_4/Z_2 all vanish. This implies that a higher-spin dS/CFT based on the Lorentzian dS_4/Z_2 action is empty. For more general interacting theories, such as ordinary gravity and Yang-Mills, we can use the free-field result to define a well-posed perturbative initial value problem in dS_4/Z_2.

• The paper demonstrates that antipodally symmetric gauge field solutions in de Sitter space enforce unique boundary conditions, resulting in vanishing n-point functions.
• It extends Vasiliev higher-spin theory to elliptic de Sitter spaces, highlighting the limitations of traditional dS/CFT correspondence models.
• The study calls for deeper investigations into reconciling holographic principles with quantum gravity in positively curved spacetimes.

An Analysis of Antipodally Symmetric Gauge Fields and Higher-Spin Gravity in de Sitter Space

The paper in question explores the mathematical underpinnings and implications of symmetric gauge fields of arbitrary spin within a de Sitter (dS) space setting, extending well beyond conventional Yang-Mills fields and gravitons to include the higher-spin fields conceptualized within Vasiliev theory. By examining antipodally symmetric solutions to field equations—those that manifest on elliptic de Sitter space $(dS_4/\mathbb{Z}_2)$—the study sets out to unravel both the nature and consequence of these symmetries and their data boundaries.

Gauge Fields in de Sitter Space

In focusing on $(dS_4/\mathbb{Z}_2)$, the paper provides a treatment of free fields that is characterized by distinct types of boundary data at infinity. Specifically, solutions to field equations exhibit an antipodal symmetry wherein the solutions on this modified space can be categorized into two distinct types, each hosting only one specific type of boundary data. This leads to a scenario where the boundary n-point functions inevitably vanish, suggesting limitations on the standard dS/CFT correspondence models when extended to these higher spin theories.

Interestingly, this property persists throughout Vasiliev theory, a higher-spin gravitational field framework that introduces an expansive tower of gauge fields. In this regime, unlike ordinary gravity or Yang-Mills theories, the interaction structure does not seem to manifest through field-boundary propagators, indicating a potentially empty or ill-defined dS/CFT when based on these classical antipodal configurations.

Implications for dS/CFT Correspondence

The implications for the dS/CFT correspondence are particularly noteworthy. While originally framed in the context of AdS spaces, there is a continuing quest to find analogous descriptions in dS space with a positive cosmological constant. Yet, the study posits that a higher-spin dS/CFT based on the Lorentzian action within dS/$Z_2$ yields results that are barren of meaning: higher-point correlation functions vanish or become ill-defined under the symmetry-preserving boundary conditions considered. As such, a straightforward adaptation of AdS/CFT models to elliptic de Sitter settings may face inherent theoretical obstructions.

Prospects for Further Research

The paper delineates a formal difference between types of boundary conditions and their propagation through elliptic de Sitter spaces. In doing so, it opens avenues for revisiting the classic holographic principles from a fresh perspective distinctly aligned with parity and antipodal symmetries. Moreover, it highlights the potential non-trivial role of smooth solutions throughout the conformally compactified de Sitter spaces, an area that might offer fruitful ground for further probing.

More broadly, the study highlights the need for a deeper theoretical understanding of elliptic de Sitter space, particularly in the context of quantum gravity, and without reliance on symmetry-breaking assumptions. Such endeavors could contribute significantly to interpreting holographic principles in positively curved spacetimes and provide insights into the enigmatic global properties of de Sitter space, especially in the light of observed cosmic horizons and horizon complementarity.

Conclusion

In summary, this work offers a comprehensive examination of the unique characteristics of antipodally symmetric fields in a modified de Sitter space framework. By evaluating the implications of these fields within higher-spin gravitation theories and the dS/CFT context, it casts a light on yet another frontier in theoretical physics—a frontier where classical intuitions about n-point functions and boundary conditions need to be critically re-evaluated in light of symmetries that are robust, yet peculiarly limiting in their present form. The pursuit for a more cohesive and informative model connecting the holographic principle with de Sitter metrics remains a promising, albeit challenging, line of exploration.