Generalizing the $\mathfrak{bms}_{3}$ and 2D-conformal algebras by expanding the Virasoro algebra

TL;DR

This paper uses Lie algebra expansion to derive and generalize 2D conformal and BMS algebras from the Virasoro algebra, introducing new infinite-dimensional symmetries relevant to gravity theories.

Contribution

It constructs new families of expanded Virasoro algebras as lifts of recently introduced algebras, extending the algebraic framework for (super)gravity models.

Findings

Derived BMS3 and 2D conformal algebras from Virasoro.

Constructed new infinite-dimensional algebra families.

Connected these algebras to gravity applications.

Abstract

By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the $\mathfrak{bms}_{3}$ algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite dimensional lifts of the so-called $\mathfrak{B}_{k}$, $\mathfrak{C}_{k}$ and $\mathfrak{D}_{k}$ algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Ka\v{c}-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.