论文标题
（超级）保形BMS $ _3 $代数
The (super)conformal BMS$_3$ algebra
论文作者
论文摘要
构建了BMS $ _ {3} $代数的共形扩展。除了为了纳入“超级共形转换”，后者的换向器和超级倾斜的换向器，严格要求在其余发电机中存在非线性项。代数似乎非常僵化，从某种意义上说，其中心扩展以及非线性项系数是由virasoro subgergra的中心电荷确定的。楔形代数对应于三个时空尺寸$ so（3,2）$中的保形组，因此整个代数也可以解释为ADS $ _ {4} $代数的无限二维非线性扩展。此外，由于lorentz subalgebra（$ sl（2，r）$）非原理嵌入了保形（楔形）代数中，根据发电机的整形重量，BMS $ _ {3} $的保形扩展可以进一步被视为$ W _ $ W _ $ w_ _ {（2,2,2,2,2,2,2,2,2,2,1）。然后，显示出BMS $ _ {3} $的共形延伸的明确规范实现，并显示出从3D中保形重力的渐近结构中出现的，并具有一组新的边界条件。还简要解决了超对称延伸。
The conformal extension of the BMS$_{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.
