Higher Spin Gravity online-club by David De Filippi

Vasiliev’s equations encode higher spin fields that interact perturbatively around a four-dimensional constantly curved spacetime through the reduction of auxiliary non-commutative dimensions. The main motivation of the presented work is the quest for suitable boundary conditions that one should impose in order to give the solutions a well defined spacetime interpretation. While we show that it is not necessary per se, the use of symbol calculus in various orderings is a useful tool to find such conditions. A notable family of reductions are the so-called holomorphic gauges, that give exact solutions to Vasiliev’s equations, but at the cost of trivial dynamics. They are however useful in that they can be used as an intermediate step, where the computation of invariants is feasible, towards a physically acceptable gauge. We construct the gauge transformation that allows to identify free propagating fields from their associated holomorphic exact solutions, for configurations that encode particles of each integer spin, and for higher-spin generalisations of the Schwarzschild black hole. We establish the link between various gauges and ordering prescriptions, and we study in particular an analytic continuation of Gaussian symbols that facilitates the analysis.