BMS modular covariance and structure constants

TL;DR

This paper explores the modular properties and structure constants of 2d BMS-invariant field theories, revealing their eigenstate thermalization behavior and connections to horizon perturbations in flat spacetime holography.

Contribution

It develops formulae for three-point structure constants of BMSFTs using modular covariance, highlighting their unique thermalization features and horizon perturbation insights.

Findings

BMSFTs follow eigenstate thermalization hypothesis with modifications.

Structure constants encode horizon perturbation information.

Limit of BTZ quasinormal modes reproduces horizon perturbation data.

Abstract

Two-dimensional (2d) field theories invariant under the Bondi-Metzner-Sachs algebra, or 2d BMSFTs in short, are putative holographic duals of Einstein gravity in 3d asymptotically flat spacetimes. When defined on a torus, these field theories come equipped with a modified modular structure. We use the modular covariance of the BMS torus two-point function to develop formulae for different three-point structure constants of the field theory. These structure constants indicate that BMSFTs follow the eigenstate thermalization hypothesis, albeit with some interesting changes to usual 2d CFTs. The singularity structures of the structure constants contain information on perturbations of cosmological horizons in 3d asymptotically flat spacetimes, which we show can also be obtained as a limit of BTZ quasinormal modes.