Unitarity and the Chaos bound (Quantum Spacetime seminar)

We study the role of unitarity in various observables in 2d CFTs. We consider 2d CFTs with large central charge in a state obtained by the insertion of an operator of large conformal dimensions at spatial infinities in the thermal state. We show that there is a violation of the chaos bound whenever the operator has negative conformal dimensions. We present a specific realisation of this situation in the holographic Chern-Simons formulation of a CFT with W3(2) symmetry also known as the Bershadsky-Polyakov algebra. We also show that the unitarity bound in CFTs which admit W3 symmetry on states with higher spin-3 charge ensures that the chaos bound is satisfied, as well as the jump in entanglement entropy during local quantum quenches remains real and finite.