Fuentealba Oscar, González Hernán A, Pérez Alfredo, Tempo David, Troncoso Ricardo
Université Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine CP231, B-1050 Brussels, Belgium.
Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Santiago 7941169, Chile.
Phys Rev Lett. 2021 Mar 5;126(9):091602. doi: 10.1103/PhysRevLett.126.091602.
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 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 AdS_{4} 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 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 three dimensions, endowed with a new set of boundary conditions. The supersymmetric extension is also briefly addressed.
构建了BMS₃代数的共形扩展。除了无穷多个“超伸缩变换”外，为了纳入超特殊共形变换，后者与超平移的对易子严格要求在其余生成元中存在非线性项。从其中心扩展以及非线性项的系数由维拉索罗子代数的中心荷决定的意义上讲，该代数似乎非常严格。楔代数对应于三维时空的共形群SO(3,2)，因此完整的代数也可解释为具有非平凡中心荷的AdS₄代数的无穷维非线性扩展。此外，由于洛伦兹子代数[sl(2,R)]非主嵌入在共形（楔）代数中，根据生成元的共形权重，BMS₃的共形扩展可进一步视为一个W(2,2,2,1)代数。然后表明，BMS₃共形扩展的一个显式正则实现源自三维共形引力的渐近结构，并赋予了一组新的边界条件。还简要讨论了超对称扩展。
