BMS Modular Diaries: Torus one-point function

TL;DR

This paper explores the modular properties of BMS-invariant 2D field theories, deriving new results like the BMS torus block and connecting them to bulk flatspace cosmological solutions.

Contribution

It introduces the BMS torus block, derives asymptotic structure constants, and links field theory results with bulk flatspace cosmology computations.

Findings

Derived the BMS torus block in large weight limit.

Obtained asymptotic structure constants for BMS primaries.

Reproduced field theory results via bulk geodesic approximation.

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.