Superconformal Bondi-Metzner-Sachs Algebra in Three Dimensions

Area of Science:

• Theoretical Physics
• High Energy Physics
• Mathematical Physics

Background:

• The BMS3 algebra is a key structure in understanding asymptotic symmetries in (2+1)-dimensional gravity.
• Previous work has explored extensions of BMS algebras, but incorporating superspecial conformal transformations presents challenges.
• Understanding nonlinear extensions is crucial for a complete description of gravitational theories in lower dimensions.

Purpose of the Study:

• To construct the conformal extension of the BMS3 algebra, including superspecial conformal transformations.
• To investigate the algebraic properties, central extensions, and nonlinear terms of this extended algebra.
• To establish a connection between this extended algebra, conformal gravity, and AdS4 algebra.

Main Methods:

• Algebraic construction of the conformal extension of the BMS3 algebra.
• Analysis of commutators involving supertranslations and superspecial conformal transformations to identify necessary nonlinear terms.
• Investigation of central extensions and their dependence on the Virasoro central charge.
• Relating the constructed algebra to known structures like the conformal group SO(3,2) and the AdS4 algebra.

Main Results:

• A rigid conformal extension of the BMS3 algebra is constructed, featuring infinite superdilatations and nonlinear terms.
• The central extensions and nonlinear coefficients are uniquely determined by the central charge of the Virasoro subalgebra.
• The algebra is shown to be an infinite-dimensional nonlinear extension of the AdS4 algebra and can be viewed as a W(2,2,2,1) algebra.

Conclusions:

• The conformal extension of BMS3 algebra exhibits a highly constrained structure, offering new insights into asymptotic symmetries.
• This construction provides a canonical realization from conformal gravity in 3D with specific boundary conditions.
• The study opens avenues for exploring supersymmetric extensions and their implications in quantum gravity.