BMS Modules in Three Dimensions

TL;DR

This paper constructs unitary representations of the BMS algebra and its higher-spin extensions in three dimensions, using ultrarelativistic limits of Virasoro and W algebras, highlighting a key difference from non-relativistic limits.

Contribution

It introduces a natural method to obtain unitary BMS representations via ultrarelativistic limits, contrasting with non-unitary non-relativistic approaches.

Findings

Ultrarelativistic limits yield unitary BMS representations.

Non-relativistic limits produce non-unitary representations.

Differences in W algebra structures under different limits.

Abstract

We build unitary representations of the BMS algebra and its higher-spin extensions in three dimensions, using induced representations as a guide. Our prescription naturally emerges from an ultrarelativistic limit of highest-weight representations of Virasoro and W algebras, which is to be contrasted with non-relativistic limits that typically give non-unitary representations. To support this dichotomy, we also point out that the ultrarelativistic and non-relativistic limits of generic W algebras differ in the structure of their non-linear terms.