Enhanced Conformal $BMS_3$ Symmetries

TL;DR

This paper introduces an enhanced conformal BMS$_{3}$ algebra derived from an extended 3D conformal gravity theory, revealing a nonlinear W algebra with potential applications in higher spin field theories.

Contribution

It presents a new nonlinear W algebra structure for asymptotic symmetries in extended conformal gravity, linking BMS$_{3}$ symmetries to higher-dimensional conformal groups.

Findings

Derivation of a nonlinear W$_{(2,2,2,2,1,1,1)}$ algebra with central extensions.

Identification of the wedge algebra as the conformal group in four dimensions, SO(4,2).

Potential framework for incorporating higher spin fields in boundary conditions.

Abstract

An enhanced version of the conformal BMS$_{3}$ algebra is presented. It is shown to emerge from the asymptotic structure of an extension of conformal gravity in 3D by Pope and Townsend that consistently accommodates an additional spin-2 field, once it is endowed with a suitable set of boundary conditions. The canonical generators of the asymptotic symmetries then span a precise nonlinear W$_{(2,2,2,2,1,1,1)}$ algebra, whose central extensions and coefficients of the nonlinear terms are completely determined by the central charge of the Virasoro subalgebra. The wedge algebra corresponds to the conformal group in four dimensions $SO(4,2)$ and therefore, enhanced conformal BMS$_{3}$ can also be regarded as an infinite-dimensional nonlinear extension of the AdS$_{5}$ algebra with nontrivial central extensions. It is worth mentioning that our boundary conditions might be considered as a starting point in order to consistently incorporate either a finite or an infinite number of conformal higher spin fields.