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Complexity in the presence of a boundary

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  • Published: 07 February 2020
  • Volume 2020, article number 51, (2020)
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Complexity in the presence of a boundary
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  • Paolo Braccia1,
  • Aldo L. Cotrone1 &
  • Erik Tonni2 

  • 464 Accesses

  • 34 Citations

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A preprint version of the article is available at arXiv.

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.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Firenze and INFN Sezione di Firenze, Via G. Sansone 1, 50019, Sesto Fiorentino, Italy

    Paolo Braccia & Aldo L. Cotrone

  2. SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136, Trieste, Italy

    Erik Tonni

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  1. Paolo Braccia
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  2. Aldo L. Cotrone
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Correspondence to Aldo L. Cotrone.

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ArXiv ePrint: 1910.03489

On leave at the Galileo Galilei Institute for Theoretical Physics, INFN National Center for Advanced Studies, Largo E. Fermi, 2, 50125 Firenze, Italy. (Aldo L. Cotrone)

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Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Braccia, P., Cotrone, A.L. & Tonni, E. Complexity in the presence of a boundary. J. High Energ. Phys. 2020, 51 (2020). https://doi.org/10.1007/JHEP02(2020)051

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  • Received: 17 October 2019

  • Accepted: 20 January 2020

  • Published: 07 February 2020

  • DOI: https://doi.org/10.1007/JHEP02(2020)051

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Keywords

  • AdS-CFT Correspondence
  • Boundary Quantum Field Theory
  • Lattice Quantum Field Theory
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