Metrics with Galilean Conformal Isometry

Abstract

The Galilean Conformal Algebra (GCA) arises in taking the non-relativistic limit of the symmetries of a relativistic Conformal Field Theory in any dimensions. It is known to be infinite-dimensional in all spacetime dimensions. In particular, the 2d GCA emerges out of a scaling limit of linear combinations of two copies of the Virasoro algebra. In this paper, we find metrics in dimensions greater than two which realize the finite 2d GCA (the global part of the infinite algebra) as their isometry by systematically looking at a construction in terms of cosets of this finite algebra. We list all possible sub-algebras consistent with some physical considerations motivated by earlier work in this direction and construct all possible higher dimensional non-degenerate metrics. We briefly study the properties of the metrics obtained. In the standard one higher dimensional "holographic" setting, we find that the only non-degenerate metric is Minkowskian. In four and five dimensions, we find families of non-trivial metrics with a rather exotic signature. A curious feature of these metrics is that all but one of them are Ricci-scalar flat.

20 pages

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Cited by in corpus (12)

• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Spatially isotropic homogeneous spacetimes
• Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
• Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations
• Ricci-flat spacetimes with l-conformal Galilei symmetry
• Homogeneous Nonrelativistic Geometries as Coset Spaces
• Super-GCA from $\mathcal{N}=(2,2)$ Super-Virasoro
• Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
• Addendum to "Super-GCA from $\mathcal{N}=(2,2)$ super-Virasoro": Super-GCA connection with tensionless strings
• Anti--de Sitter/ boundary conformal field theory correspondence in the non-relativistic limit
• Wess-Zumino-Witten Model for Galilean Conformal Algebra
• Highest weight representations and Kac determinants for a class of conformal Galilei algebras with central extension