Description
We place new constraints on the landscape of 2d conformal field theories with higher spin currents, and on higher spin theories in AdS_3, using Lorentzian bootstrap methods. We show that unitary 2d CFTs with large central charge, light primary operators and a finite tower of higher spin currents cannot exist, and likewise for their putative AdS_3 dual theories of higher spin gravity. Theories with infinite towers of currents evade this conclusion, consistent with a potential embedding into string theory.
