|Gravitons, BRST-BMS4 Symmetry and its Cocycles from Horizontality Conditions
|Laurent Baulieu, Laboratoire de Physique Théorique et Hautes Énergies (LPTH
|Event Type: Special Seminar
|Time: 1:00 PM - 2:15 PM
|Location: 726 Broadway, 940, CCPP Seminar
|Abstract: The BRST structure of the extended Bondi-Metzner-Sachs symmetry group of asymptotically flat manifolds is studied using the recently introduced framework of Beltrami field parametrization of four-dimensional metrics. The latter has interesting properties. In particular, it allows to geometrically define as fundamental fields the two physical degrees of freedom of asymptotic perturbative gravitons of asymptotically flat spaces. They are identified as excitations of the Beltrami differential of the asymptotic celestial sphere, enabling quite suggestive formula for the memory effect. The graded BRST BMS4 nilpotent differential operator that classically define the BMS symmetry transformations is actually based on four horizontality conditions. A number of BRST BMS4 cocycles can then be found, connected by descent equations. This indicates the possibility of anomalies for three-dimensional Lagrangian theories possibly built from the principle of BRST-BMS4 invariance in the null boundaries $cal I ^pm$ of asymptotically flat spaces. Remarkably, the BMS anomaly cocycle $delta^1_3$ has a simplest and natural expression. Its descendants, $delta^2_2$ that can be associated with the occurrence of a central charge in Hamiltonian formalism, $delta^3_1$ and $delta^4_0$ have much less suggestive expressions that encode some subtilities of the four dimensional nature of the BMS4 symmetry.