Circuit Complexity for Carrollian Conformal (BMS) Field Theories

TL;DR

This paper investigates the construction of Nielsen's circuit complexity for 2D Carrollian (BMS) field theories, revealing a richer structure than geometric actions and connecting results to flat holography and BMS symmetries.

Contribution

It introduces a refined intrinsic approach to compute circuit complexity in BMS field theories, overcoming limitations of the limiting approach and uncovering new structural insights.

Findings

Complexity functional expressed via BMS co-adjoint orbit

Refined intrinsic approach captures richer symmetry structure

Solutions connect to existing literature on flat holography

Abstract

We systematically explore the construction of Nielsen's circuit complexity to a non-Lorentzian field theory keeping in mind its connection with flat holography. We consider a 2d boundary field theory dual to 3d asymptotically flat spacetimes with infinite-dimensional BMS_3 as the asymptotic symmetry algebra. We compute the circuit complexity functional in two distinct ways. For the Virasoro group, the complexity functional resembles the geometric action on its co-adjoint orbit. Using the limiting approach on the relativistic results, we show that it is possible to write BMS complexity in terms of the geometric action on BMS co-adjoint orbit. However, the limiting approach fails to capture essential information about the conserved currents generating BMS supertranslations. Hence, we refine our analysis using the intrinsic approach. Here, we use only the symmetry transformations and group product laws of BMS to write the complexity functional. The refined analysis shows a richer structure than only the geometric action. Lastly, we extremize and solve the equations of motion (for a simple solution) in terms of the group paths and connect our results with available literature.