Flat Holography: Aspects of the dual field theory (1609.06203v1)

Abstract: Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk - 2d boundary case and then focus on the 4d bulk - 3d boundary example, where the symmetry in question is the infinite dimensional BMS4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under the conformal Carroll group in D=4. We explore the different sectors within these Carrollian gauge theories and investigate the symmetries of the equations of motion to find that an infinite ultra-relativistic conformal structure arises in each case.

Overview of Flat Holography and the Dual Field Theory

This paper provides a detailed examination of the theoretical framework for flat holography, focusing on field theories that may serve as duals to asymptotic flat spacetimes. The fundamental idea explored here is the relationship between field theories in D dimensions and (D+1)-dimensional flat spaces, modulated by the asymptotic symmetries of the latter. The authors offer a systematic approach starting with the well-explored 3D bulk and 2D boundary case and then progress to analyze the more complex scenario involving 4D bulk and 3D boundaries.

A major component of this paper is the exploration of the Bondi-Metzner-Sachs (BMS) group—an infinite-dimensional symmetry group relevant in four-dimensional flat spacetimes. Previous studies have typically focused on the more manageable three-dimensional cases, where insights from AdS/CFT have been readily aligned. This paper investigates the challenges and nuances in extending such frameworks to higher dimensions, specifically 4D flat space holography.

Key Findings

1. BMS 4 Algebra and Representation: The authors delve into the construction of the highest weight representations of the BMS 4 algebra. The algebra is characterized by infinite dimensions and challenges traditional approaches to understanding holographic dualities. Through this representation, the authors calculate two and three-point correlation functions of BMS primary fields, discovering that these are surprisingly identical to those found in 2D relativistic conformal field theories. This indicates potential parallels and suggest that the dual to 4D Minkowski spacetime could manifest as a 2D conformal field theory.
2. Dimensions and Symmetry: Further exploration into 3D theories as candidates for holographic duals to 4D Minkowski spacetime shows a reliance on two Virasoro generators but not on the supertranslation labeling, proposing that these states might align with modules of two Virasoro algebras.
3. Ultra-Relativistic Limits: The paper describes a novel approach by utilizing ultra-relativistic contractions to theorize about conformal Carroll groups in higher dimensions—specifically constructing conformal Carroll algebras with infinite extensions in dimensions higher than three. Their approach opens new prospects for understanding infinite symmetries that have potential implications for field theories associated with flat spacetime holography.
4. Carrollian Gauge Theories: By examining the ultra-relativistic regime of gauge theories—like electrodynamics and Yang-Mills—the authors exhibit fields that demonstrate invariance under conformal Carroll groups. They confirm that even sectors within these Carrollian gauge theories exhibit infinite ultra-relativistic conformal structures, making them prototypes of field theories dual to 5D Minkowski spacetimes described by extended BMS algebras.

Implications and Future Directions

This paper's insights fundamentally enrich the theoretical groundwork laid for holography concerning flat spacetimes. The findings suggest that further developments in both ultra-relativistic limits and Carrollian representations have vast implications not only for holography but also for understanding gravitational memory effects and potentially new resolutions for the black hole information paradox.

The implications of flat holography on quantum gravity and related areas demand deeper examination and practical applications. Future work suggested by the authors could include extending this research to incorporate matter fields and formulation of action principles in the framework of Carrollian manifolds. These fields represent an exciting frontier for theoretical physics, promising advancements that could inform well-known problems ranging from black hole theory to cosmological modeling.

In summary, this paper's contribution—a thorough executable schema for analyzing flat holography—sets the stage for future explorations in field theories and infinite-dimensional symmetries, helping bridge the abstractions of theoretical constructs with tangible quantum gravity applications.