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

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• Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis
• Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
• Holography in CGHS supergravity
• 1/c deformations of AdS${}_3$ boundary conditions and the Dym hierarchy
• Enhanced Conformal $BM{S}_3$ Symmetries
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• 3-dimensional $\Lambda$-BMS Symmetry and its Deformations