CFT to BMS: complexity and OTOC

Abstract

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 fieldtheory and following through at the quantum level using an oscillator representation ofstates, one can show the CFT2vacuum evolves smoothly into a BMS3vacuum in the form ofa squeezed state. Computing circuit complexity of this transmutation using the covariancematrix approach shows clear divergences when the BMS point is hit or equivalently whenthe target state becomes a boundary state. We also find similar behaviour of the circuitcomplexity calculated from methods of information geometry. Furthermore, we discussthe hamiltonian evolution of the system and investigate Out-of-time-ordered correlators(OTOCs) and operator growth complexity, both of which turn out to scale polynomiallywith time at the BMS point