BMS Characters and Modular Invariance

Abstract

We construct the characters for the highest weight representations of the 3d Bondi-Metzner-Sachs (BMS${}_3$) algebra. We then use these to construct the partition function and show how to use BMS modular transformations to obtain a density of primary states. The entropy thus obtained accounts for the principle part of the entropy obtained from the BMS-Cardy formula. This suggests that BMS primaries capture most of the entropy of Flat Space Cosmologies, which are the flatspace analogues of BTZ black holes in AdS${}_3$. We reproduce our character formula by looking at singular limits from 2d CFT characters and find that our answers are identical to the characters obtained for the very different induced representations. We offer an algebraic explanation to this arising from a (to the best of our knowledge) novel automorphism in the parent 2d CFT.

arXiv comment39 pages, 2 figures, ordering of the sections changed, figure 1 changed, references added, footnotes added, typos corrected. Matched published version

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• A Tale of Three. Tensionless strings and vacuum structure
• A BMS-invariant free scalar model
• Geometric actions and flat space holography
• Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Most general theory of 3d gravity: Covariant phase space, dual diffeomorphisms, and more
• On Galilean conformal bootstrap
• BMS Modular Diaries: Torus one-point function
• Semi-classical BMS-blocks from the Oscillator Construction
• Universal sectors of two-dimensional Carrollian CFTs
• Supersymmetric Localization on dS: Sum over topologies
• Character of the highest weight module of BMS algebra realized on codimensional-two boundary
• Modular matrices of 2d Carrollian and warped CFTs