From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators

We probe the contraction from 2d relativistic CFTs to theories with Bondi-Metzner-Sachs (BMS) symmetries, or equivalently conformal Carroll symmetries, using diagnostics of quantum chaos. Starting from an ultrarelativistic limit on a relativistic scalar field theory and following through at the quantum level using an oscillator representation of states, one can show the CFT 2 vacuum evolves smoothly into a BMS 3 vacuum in the form of a squeezed state. Computing circuit complexity of this transmutation using the covariance matrix approach shows clear divergences when the BMS point is hit or equivalently when the target state becomes a boundary state. We also find similar behavior of the circuit complexity calculated from methods of information geometry. Furthermore, we discuss the Hamiltonian evolution of the system and investigate out-of-time-ordered correlators and operator growth complexity, both of which turn out to scale polynomially with time at the BMS point.