On the Spectrum of Pure Higher Spin Gravity

One of the very unique properties of AdS_3 spacetimes is that we can introduce a finite number of massless higher spin fields without yielding an inconsistent theory. In this talk, we would like to comment on what the spectrum of these theories looks like: from the known contribution of the light spectrum, that corresponds to the vacuum character of the W_N algebra, we can use modular invariance to constraint the heavy spectrum of the theory. However, in doing so, we find negative norm states, inconsistent with unitarity. We propose a possible cure by adding light states that can be interpreted as massive particles with a conical defect associated to them, and study what scenario we are left with. The results that we will revisit are those presented in 2009.01830.