Semi-simple enlargement of the $\mathfrak{bms}_3$ algebra from a $\mathfrak{so}(2,2)\oplus\mathfrak{so}(2,1)$ Chern-Simons theory

TL;DR

This paper develops a BMS-like framework for a Chern-Simons theory based on the semi-simple AdS-Lorentz algebra, revealing an asymptotic symmetry algebra isomorphic to three Virasoro copies, and explores its flat limit.

Contribution

It introduces a new BMS-like ansatz for the AdS-Lorentz algebra in Chern-Simons theory and characterizes its asymptotic symmetry algebra as three Virasoro copies.

Findings

The ansatz encompasses all relevant stationary solutions.

The asymptotic symmetry algebra is a semi-simple enlargement of ms_3, isomorphic to three Virasoro algebras.

The flat limit of the theory is explicitly analyzed.

Abstract

In this work we present a BMS-like ansatz for a Chern-Simons theory based on the semi-simple enlargement of the Poincar\'e symmetry, also known as AdS-Lorentz algebra. We start by showing that this ansatz is general enough to contain all the relevant stationary solutions of this theory and provides with suitable boundary conditions for the corresponding gauge connection. We find an explicit realization of the asymptotic symmetry at null infinity, which defines a semi-simple enlargement of the $\mathfrak{bms}_3$ algebra and turns out to be isomorphic to three copies of the Virasoro algebra. The flat limit of the theory is discussed at the level of the action, field equations, solutions and asymptotic symmetry.