The BMS group in $D= 6$ spacetime dimensions

The asymptotic structure of gravity in $D=6$ spacetime dimensions is described at spatial infinity in the asymptotically flat context through Hamiltonian (ADM) methods. Special focus is given on the BMS supertranslation subgroup. It is known from previous studies that the BMS group contains more supertranslations as one goes from $D=4$ to $D=5$. Indeed, while the supertranslations are described by one single function of the angles in $D=4$, four such functions are neeeded in $D=5$. We consider the case $D=6$ with the aim of determining whether the number of supertranslations keeps increasing with the dimension or remains equal to the number found in $D=5$. We show that even though there is apparent room for more supertranslations, their number remains equal to the $D=5$ value (four): the potentially new supertranslations turn out to define proper gauge transformations corresponding to a redundancy in the description of the system. Critical in the analysis are the boundary conditions chosen to yield a well-defined canonical formalism. Given the computational (but not conceptual) complexity as one increases the dimension, we explicitly discuss the linearized theory and argue that asymptotically, this analysis provides the correct picture. We conclude by considering higher spacetime dimensions where we indicate that the number of physically relevant supertranslations remains equal to four independently of the dimension $\geq 5$.