Gravity from (A)dS Yang-Mills: a natural reduction (2501.17574v2)

Abstract: We investigate the relationship between a one-parameter family of (anti)-de Sitter Yang-Mills models and Einstein-Palatini gravity with matter, realized through In\"o\"nu-Wigner contraction of the (A)dS algebra. By setting the gauge group parameter $\alpha$ to zero, the gauge transformation of the potential becomes consistent with the transformation properties of the tetrad form and spin connection. We show that a sector of the Yang-Mills dynamics exists where the gauge fields acquire a geometric interpretation, and the full Yang-Mills symmetry gives rise to diffeomorphisms and local Lorentz transformations. Finally, the corresponding dynamics is consistent with unimodular gravity.

• The paper presents a novel method where the Yang-Mills action, via Inönü-Wigner contraction, reproduces Einstein-Palatini gravity.
• It details the symmetry reduction from full (A)dS gauge invariance to the diffeomorphism and local Lorentz symmetries of general relativity.
• The work confirms theoretical consistency by preserving differential identities, suggesting promising pathways for quantum gravity research.

Insights into Gravity from (A)dS Yang-Mills Models and Einstein-Palatini Gravity

This paper explores the fascinating intersection of gauge theories and gravity, specifically formulating gravity as a gauge theory using the (anti)-de Sitter ((A)dS) Yang-Mills models. The work explores how the Einstein-Palatini formulation of gravity, which typically requires the separation of tetrads and spin connections as independent fields, can emerge from a one-parameter family of (A)dS Yang-Mills models through an Inönü-Wigner contraction of the (A)dS algebra to the Poincaré algebra.

Summary of Key Findings

1. Yang-Mills to Gravity Transition: The authors present a method where the Yang-Mills action corresponding to a specific parameter setting reproduces the Einstein equations of general relativity in the limit that the parameter tends to zero. This process involves understanding how the gauge fields transform into tetrads and Lorentz connections, foundational components of the Einstein-Palatini formalism.
2. Symmetry Reduction: The full gauge symmetry of the initial Yang-Mills action gives rise to invariance under diffeomorphisms and local Lorentz transformations in the limit, which is essential for aligning with the symmetries of general relativity. The paper delineates how the transition alters the interpretation of gauge fields, facilitating a consistent gravitational theory framework without modifying the Einstein-Palatini dynamics.
3. Differential Identities and Bianchi Consistency: Critical to this transition are differential identities akin to Bianchi identities in general relativity, ensuring that curvature and torsion maintain their gravitational interpretations. The preservation of these identities across the contraction process underscores the theoretical consistency of mapping between the gauge and gravitational theories.
4. Novelty of Invariance: The authors highlight that a crucial aspect of their methodology is preserving the form invariance of the action across the contraction limit. This preservation assists in smoothly deriving the gravitational Lagrangian, manifesting as a standard description in the tetradic-Palatini framework.
5. Comparison with Existing Frameworks: The paper compares its results with previous literature, noting differences such as the role of torsion and curvature contributions and providing insights into the historical challenges of unifying gravity within a gauge-theoretic perspective.

Theoretical and Practical Implications

The research presents both theoretical advancements and practical implications. Theoretically, it suggests a framework where gravity can be consistently expressed as a gauge theory, potentially offering new routes for its quantization by leveraging gauge theoretical techniques known from other fields like particle physics.

Practically, the alignment with existing gravitational frameworks and the potential insights into cosmological phenomena (via the cosmological constant's role and gauge group selection) provide a fertile ground for exploring new solutions in cosmology and black hole physics. Furthermore, the methodology offers pathways for addressing fundamental challenges in theoretical physics, including the quest for a unified description of all fundamental forces.

Speculations on Future Developments

Future work may focus on integrating matter into this framework, addressing symmetry breaking phenomena, and encountering new gauge-theoretical formulations that might reconcile quantum mechanics and general relativity. These paths could facilitate novel approaches to solve gravitational singularities and inflationary dynamics within a consistent gauge-theoretic formulation.

Overall, the paper introduces a significant methodological advancement in understanding gravity through gauge theories, offering both a reinterpretation of classical concepts and a bridge toward potential quantum gravity theories. The intersection of contraction methods and gauge theoretical constructs heralds a promising frontier for continued exploration.