TY - JOUR

T1 - Superconformal Bondi-Metzner-Sachs Algebra in Three Dimensions

AU - Fuentealba, Oscar

AU - González, Hernán A.

AU - Pérez, Alfredo

AU - Tempo, David

AU - Troncoso, Ricardo

N1 - Funding Information:
We thank Marcela Cárdenas, Ricardo Caroca, Joaquim Gomis, Daniel Grumiller, Marc Henneaux, Javier Matulich, Fábio Novaes, Miguel Pino, and Pablo Rodríguez for useful discussions. O. F. holds a “Marina Solvay” fellowship. This work was partially supported by the ERC Advanced Grant “High-Spin-Grav,” by FNRS-Belgium (conventions FRFC PDRT.1025.14 and IISN 4.4503.15). This research has been partially supported by FONDECYT Grants No. 1171162, No. 1181031, No. 1181496, and No. 11190427. The Centro de Estudios Científicos (CECs) is funded by the Chilean Government through the Centers of Excellence Base Financing Program of Conicyt.
Publisher Copyright:
© 2021 authors.

PY - 2021/3/4

Y1 - 2021/3/4

N2 - The conformal extension of the BMS3 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 coefficients of the nonlinear terms 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 AdS4 algebra with nontrivial central charges. Moreover, since the Lorentz subalgebra [sl(2,R)] is nonprincipally embedded within the conformal (wedge) algebra, according to the conformal weight of the generators, the conformal extension of BMS3 can be further regarded as a W(2,2,2,1) algebra. An explicit canonical realization of the conformal extension of BMS3 is then shown to emerge from the asymptotic structure of conformal gravity in three dimensions, endowed with a new set of boundary conditions. The supersymmetric extension is also briefly addressed.

AB - The conformal extension of the BMS3 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 coefficients of the nonlinear terms 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 AdS4 algebra with nontrivial central charges. Moreover, since the Lorentz subalgebra [sl(2,R)] is nonprincipally embedded within the conformal (wedge) algebra, according to the conformal weight of the generators, the conformal extension of BMS3 can be further regarded as a W(2,2,2,1) algebra. An explicit canonical realization of the conformal extension of BMS3 is then shown to emerge from the asymptotic structure of conformal gravity in three dimensions, endowed with a new set of boundary conditions. The supersymmetric extension is also briefly addressed.

UR - http://www.scopus.com/inward/record.url?scp=85102205287&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.126.091602

DO - 10.1103/PhysRevLett.126.091602

M3 - Article

C2 - 33750147

AN - SCOPUS:85102205287

SN - 0031-9007

VL - 126

JO - Physical Review Letters

JF - Physical Review Letters

IS - 9

M1 - 091602

ER -