Complexity in the presence of a boundary

TL;DR

This paper investigates how boundaries affect circuit complexity in 2D theories using holographic duality and harmonic chains, revealing boundary-induced divergences and discontinuous complexity changes.

Contribution

It analyzes the impact of boundaries on complexity in holographic and harmonic chain models, highlighting divergences and discontinuities not previously detailed.

Findings

Boundary introduces subleading logarithmic divergence in complexity expansion.

Holographic subregion complexity can change discontinuously with subregion configuration.

Different complexity proposals show consistent boundary effects except for CA.

Abstract

The effects of a boundary on the circuit complexity are studied in two dimensional theories. The analysis is performed in the holographic realization of a conformal field theory with a boundary by employing different proposals for the dual of the complexity, including the "Complexity = Volume" (CV) and "Complexity = Action" (CA) prescriptions, and in the harmonic chain with Dirichlet boundary conditions. In all the cases considered except for CA, the boundary introduces a subleading logarithmic divergence in the expansion of the complexity as the UV cutoff vanishes. Holographic subregion complexity is also explored in the CV case, finding that it can change discontinuously under continuous variations of the configuration of the subregion.