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 Kač–Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.
Highlights
Infinite-dimensional symmetries play a prominent role in different areas of physics
When 3D Einstein gravity with negative cosmological constant is formulated as a Chern–Simons theory, it can be written as an S L(2, R) WZW model once the Hamiltonian constraints are solved within the action
In the case of vanishing cosmological constant, the bms3 algebra is found as the asymptotic symmetry of Einstein gravity at null infinity [18]. This algebra is given by the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an abelian ideal of super translations and can be obtained as an Inönü– Wigner (IW) contraction [19,20] of the centrally extended conformal algebra in two dimensions in the very same way as the Poincaré symmetry follows from the AdS3 symmetry [21]
Summary
Infinite-dimensional symmetries play a prominent role in different areas of physics. In particular, symmetries of the Virasoro type have had remarkable applications in twodimensional field theory, fluid mechanics, string theory, soliton theory and gravity among others. In the case of vanishing cosmological constant, the bms algebra is found as the asymptotic symmetry of Einstein gravity at null infinity [18] This algebra is given by the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an abelian ideal of super translations and can be obtained as an Inönü– Wigner (IW) contraction [19,20] of the centrally extended conformal algebra in two dimensions in the very same way as the Poincaré symmetry follows from the AdS3 symmetry [21]. In this paper we put forward such study and present new families of infinite-dimensional algebras that can be obtained by applying the semigroup expansion mechanism to the Virasoro algebra.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
