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Resolving modular flow: a toolkit for free fermions
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 21 December 2020

Resolving modular flow: a toolkit for free fermions

  • Johanna Erdmenger1,
  • Pascal Fries1,
  • Ignacio A. Reyes  ORCID: orcid.org/0000-0001-5456-55902 &
  • …
  • Christian P. Simon1 

Journal of High Energy Physics volume 2020, Article number: 126 (2020) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

Modular flow is a symmetry of the algebra of observables associated to space-time regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is known about its action beyond highly symmetric cases. The key idea of this work is to introduce a new formula for modular flows for free chiral fermions in 1 + 1 dimensions, working directly from the resolvent, a standard technique in complex analysis. We present novel results — not fixed by conformal symmetry — for disjoint regions on the plane, cylinder and torus. Depending on temperature and boundary conditions, these display different behaviour ranging from purely local to non-local in relation to the mixing of operators at spacelike separation. We find the modular two-point function, whose analytic structure is in precise agreement with the KMS condition that governs modular evolution. Our ready-to-use formulae may provide new ingredients to explore the connection between spacetime and entanglement.

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Author information

Authors and Affiliations

  1. Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074, Würzburg, Germany

    Johanna Erdmenger, Pascal Fries & Christian P. Simon

  2. Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476, Potsdam-Golm, Germany

    Ignacio A. Reyes

Authors
  1. Johanna Erdmenger
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  2. Pascal Fries
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  3. Ignacio A. Reyes
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Correspondence to Ignacio A. Reyes.

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ArXiv ePrint: 2008.07532

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Erdmenger, J., Fries, P., Reyes, I.A. et al. Resolving modular flow: a toolkit for free fermions. J. High Energ. Phys. 2020, 126 (2020). https://doi.org/10.1007/JHEP12(2020)126

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  • Received: 29 September 2020

  • Accepted: 10 November 2020

  • Published: 21 December 2020

  • DOI: https://doi.org/10.1007/JHEP12(2020)126

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Keywords

  • Conformal Field Theory
  • Field Theories in Lower Dimensions
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