BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries (1203.5795v2)

Abstract: The asymptotic group of symmetries at null infinity of flat spacetimes in three and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS) group. This has recently been shown to be isomorphic to non-relativistic conformal algebras in one lower dimension, the Galilean Conformal Algebra (GCA) in 2d and a closely related non-relativistic algebra in 3d [1]. We provide a better understanding of this surprising connection by providing a spacetime interpretation in terms of a novel contraction. The 2d GCA, obtained from a linear combination of two copies of the Virasoro algebra, is generically non-unitary. The unitary subsector previously constructed had trivial correlation functions. We consider a representation obtained from a different linear combination of the Virasoros, which is relevant to the relation with the BMS algebra in three dimensions. This is realised by a new space-time contraction of the parent algebra. We show that this representation has a unitary sub-sector with interesting correlation functions. We discuss implications for the BMS/GCA correspondence and show that the flat space limit actually induces precisely this contraction on the boundary conformal field theory. We also discuss aspects of asymptotic symmetries and the consequences of this contraction in higher dimensions.

• The paper establishes a connection between the BMS group and GCA through a novel contraction method, underpinning a new framework for flat-space holography.
• The authors demonstrate a unitary sub-sector in the 2D GCA, supported by non-trivial correlation functions that resolve earlier issues of non-unitarity.
• Their analysis extends the AdS/CFT paradigm, providing insights into flat-space limits and offering new pathways for understanding quantum gravitational dynamics.

Analysis of "BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries"

The academic paper titled "BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries" by Arjun Bagchi and Reza Fareghbal provides a comprehensive examination of the linkage between the asymptotic symmetry groups of flat spacetimes, specifically the Bondi-Metzner-Sachs (BMS) group, and non-relativistic conformal algebras such as the Galilean Conformal Algebra (GCA). This paper is grounded in the desire to extend the success of the AdS/CFT correspondence, which has so effectively linked anti-de Sitter spaces with conformal field theories, into the domain of flat-space holography—a pursuit initiated by the recognition of the BMS group's infinite-dimensional symmetry.

Summary and Key Insights

Main Contributions and Findings

1. Connection between BMS and GCA: The paper elaborates on the surprising alignment between the BMS group, characterizing symmetries at null infinity of flat spacetimes, and the GCA in lower dimensions. This association is primarily realized through a novel contraction procedure that highlights a representation of the GCA obtained from variants of the Virasoro algebra.
2. Representation and Unitarity: Bagchi and Fareghbal investigate a specific representation of the 2D GCA, gained via an alternative to traditional spacetime scalings, emphasizing its unitary sub-sector. Notably, they demonstrate the presence of non-trivial correlation functions within this sector, addressing prior issues of non-unitarity in related theories.
3. Flat Space Holography: The paper forwards the notion that the flat space limit instigates a contraction paradigm on the boundary conformal field theory, a crucial step towards elucidating a holographic principle for flat spacetimes paralleling the AdS/CFT framework.
4. Technical Analysis and Extensions: Through spacetime contraction and algebraic manipulations, the authors convey how certain limits of AdS mathematics naturally lead to the flat space symmetries observed, asserting the flat space limit's reliability and potential to forge new understandings in holographic theories.

Implications and Theoretical Developments

The detailed analyses of non-relativistic algebras and asymptotic symmetries conducted within the paper not only reaffirm the robustness of the BMS/GCA correspondence but also suggest pathways towards a more comprehensive framework for flat-space holography. There are significant implications for understanding both the quantum properties of flat spacetime and broader gravitational theories, possibly impacting areas such as the formulation of the S-matrix in flat-spacetime contexts.

Speculation on Future Developments

The establishment of a robust theoretical basis for correlating BMS symmetries with GCA suggests that further exploration into higher-dimensional analogues could reveal deep connections between different spacetime geometries and lower-dimensional field theories. Extensions of this work may eventually make it feasible to apply these principles to more practical aspects of string theory, non-relativistic condensed matter systems, or higher-dimensional gravitational models.

In conclusion, this paper signifies a pivotal contribution to the understanding of symmetries in gravitational physics and stands as a foundational stepping stone for expanding the horizons of flat-space holography. The bridging of BMS symmetries and GCAs offers both a conceptual parallel to the celebrated AdS/CFT paradigm and potential insights into the quantum gravitational landscape.