From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
arXiv:2205.15338 · doi:10.1103/PhysRevD.106.126022
Abstract
We probe the contraction from 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 vacuum evolves smoothly into a BMS 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 behaviour 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 (OTOCs) and operator growth complexity, both of which turn out to scale polynomially with time at the BMS point.
arXiv commentV3: To appear in PRD. Change of title has been implemented by the editors. It was simply titled "CFT to BMS: Complexity and OTOC" before
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