Scalar Two-Point Functions in Anti-de Sitter Space Enable Global AdS Invariance

Understanding the behaviour of quantum fields in anti-de Sitter space, a theoretical universe with unique geometric properties, remains a central challenge in theoretical physics, with implications for gravity and quantum field theory. Ugo Moschella, from the Dipartimento di Scienza e Alta Tecnologia and INFN sez. di Milano, and colleagues, now present a new way to represent fundamental quantities called two-point functions within this universe, offering a coordinate-free and manifestly covariant approach. This construction utilises a novel mathematical framework based on chiral cones, and importantly, allows researchers to connect calculations in Euclidean and Lorentzian quantum field theory, simplifying the process of translating theoretical predictions into potentially observable results. By achieving this connection while preserving the full symmetry of anti-de Sitter space, the team clarifies a long-standing problem and provides a powerful tool for exploring the foundations of quantum gravity.

Holomorphic Decomposition in Anti-de Sitter Space

This work delves into the mathematical and physical foundations of quantum field theory in anti-de Sitter (AdS) space, with connections to cosmology, holography, and even Pythagorean philosophy. The central argument is that a consistent and physically meaningful quantum field theory can be constructed in AdS space by carefully considering the mathematical properties of the space itself, particularly its hyperbolic geometry. The author emphasizes the importance of holomorphic decomposition, a key mathematical tool for simplifying calculations and revealing underlying symmetries, and defining appropriate plane wave solutions that satisfy a spectral condition crucial for a physically viable theory. The author also draws parallels between AdS space and cosmological models, suggesting that insights from AdS QFT can inform our understanding of the universe and the holographic principle.,.

Chiral Cones and AdS Scalar Function Representation

Scientists have developed a novel method for representing scalar two-point functions in d-dimensional anti-de Sitter spacetime, constructing a manifestly covariant and coordinate-free plane representation. This work centers on a new class of holomorphic plane waves defined globally on the universal covering of AdS via chiral cones within the complex null cone, offering a fundamentally different approach to analyzing quantum fields in this curved spacetime. By imposing stringent conditions, AdS invariance, locality, positive definiteness, and a spectral condition, the team obtained integral representations that successfully reproduce standard maximally analytic solutions expressed using Legendre functions of the second kind. This core achievement lies in a specific integral formula, representing the two-point function of a massive scalar field, which does not separate space and time variables or rely on any particular coordinate system and reveals the primitive analyticity domain of the two-point function.,.

AdS Spacetime Two-Point Functions via Holomorphic Planes

Scientists have constructed a manifestly covariant and coordinate-free representation of scalar two-point functions within anti-de Sitter spacetime, achieving a breakthrough in understanding field theory in curved space. This work centers on a new class of holomorphic plane waves defined globally on the universal covering of the AdS space via chiral cones within the complex null cone, providing a powerful new tool for calculations. By imposing conditions of AdS invariance, locality, positive definiteness, and a spectral condition, the team obtained integral representations that successfully reproduce standard maximally analytic solutions using Legendre functions of the second kind. The resulting two-point functions diagonalize into a superposition of Minkowski correlators, revealing a deep connection between Euclidean and Lorentzian AdS field theory and enabling a consistent Wick rotation of Feynman diagrams while preserving full AdS covariance.,.

Covariant Scalar Two-Point Functions in AdS Space

This work establishes a new, manifestly covariant representation of scalar two-point functions within anti-de Sitter spacetime. Researchers constructed a plane-wave representation based on holomorphic functions defined globally on the universal covering of the AdS space, utilizing chiral cones within the complex null cone. By imposing constraints of AdS invariance, locality, positive definiteness, and spectral conditions, the team obtained integral representations that reproduce standard maximally analytic solutions, expressed using Legendre functions. The resulting two-point functions diagonalize into a superposition of Minkowski correlators, revealing a direct link between Euclidean and Lorentzian AdS field theory and enabling a consistent Wick rotation of Feynman diagrams while preserving full AdS covariance.