The (super)conformal BMS${}_3$ algebra

Abstract

The conformal extension of the BMS${}_3$ algebra is constructed. Apart from an infinite number of 'superdilatations,' in order to incorporate 'superspecial conformal transformations,' the commutator of the latter with supertranslations strictly requires the presence of nonlinear terms in the remaining generators. The algebra appears to be very rigid, in the sense that its central extensions as well as the nonlinear terms coefficients become determined by the central charge of the Virasoro subalgebra. The wedge algebra corresponds to the conformal group in three spacetime dimensions $SO(3,2)$, so that the full algebra can also be interpreted as an infinite-dimensional nonlinear extension of the AdS${}_4$ algebra with nontrivial central charges. Moreover, since the Lorentz subalgebra ($sl(2,R)$) is non-principally embedded within the conformal (wedge) algebra, according to the conformal weight of the generators, the conformal extension of BMS${}_3$ can be further regarded as a $W_{(2,2,2,1)}$ algebra. An explicit canonical realization of the conformal extension of BMS${}_3$ is then shown to emerge from the asymptotic structure of conformal gravity in 3D, endowed with a new set of boundary conditions. The supersymmetric extension is also briefly addressed.

17 pages, no figures

References in corpus (17)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Asymptotic symmetries and subleading soft graviton theorem
• New symmetries for the Gravitational S-matrix
• Flat-Space Chiral Gravity
• Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity
• Generalized Black Holes in Three-dimensional Spacetime
• Asymptotic symmetries and dynamics of three-dimensional flat supergravity
• Super-BMS${}_3$ algebras from $\mathcal{N}=2$ flat supergravities
• Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS${}_3$ and nonlinear energy bounds
• Flat space (higher spin) gravity with chemical potentials
• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Static spherically symmetric solutions for conformal gravity in three dimensions
• N=4 Supersymmetric BMS3 algebras from asymptotic symmetry analysis
• Spectral Flow in 3D Flat Spacetimes
• Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity
• Extended Supersymmetric BMS${}_3$ algebras and Their Free Field Realisations
• W-algebra W(2,2) and the vertex operator algebra L(1/2,0)\otimes L(1/2,0)