BMS Modular Diaries: Torus one-point function

Abstract

Two dimensional field theories invariant under the Bondi-Metzner-Sachs (BMS) group are conjectured to be dual to asymptotically flat spacetimes in three dimensions. In this paper, we continue our investigations of the modular properties of these field theories. In particular, we focus on the BMS torus one-point function. We use two different methods to arrive at expressions for asymptotic structure constants for general states in the theory utilising modular properties of the torus one-point function. We then concentrate on the BMS highest weight representation, and derive a host of new results, the most important of which is the BMS torus block. In a particular limit of large weights, we derive the leading and sub-leading pieces of the BMS torus block, which we then use to rederive an expression for the asymptotic structure constants for BMS primaries. Finally, we perform a bulk computation of a probe scalar in the background of a flatspace cosmological solution based on the geodesic approximation to reproduce our field theoretic results.

arXiv comment101 pages, 4 figures, 12 appendices; v2: typos and minor errors corrected, references added, acknowledgement updated, matches journal version

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Cited by in corpus (7)

• AdS Witten Diagrams to Carrollian Correlators
• The Shadow Formalism of Galilean CFT${}_2$
• Circuit Complexity for Carrollian Conformal (BMS) Field Theories
• Semi-classical BMS-blocks from the Oscillator Construction
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• Universal sectors of two-dimensional Carrollian CFTs
• Modular matrices of 2d Carrollian and warped CFTs