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

TL;DR

This paper investigates the transition from 2D relativistic CFTs to theories with BMS symmetries, analyzing quantum chaos diagnostics, circuit complexity, and operator growth, revealing divergences and polynomial scaling at the BMS point.

Contribution

It introduces a detailed analysis of the contraction from 2D CFTs to BMS-invariant theories using quantum chaos diagnostics and complexity measures, highlighting new behaviors at the BMS point.

Findings

Circuit complexity diverges at the BMS point.

OTOCs and operator growth scale polynomially at the BMS point.

Vacuum states evolve smoothly into squeezed states during contraction.

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 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 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.