First law of entanglement rates from holography

Andy O’Bannon, Jonas Probst, Ronnie Rodgers, and Christoph F. Uhlemann
Phys. Rev. D 96, 066028 – Published 21 September 2017

Abstract

For a perturbation of the state of a conformal field theory (CFT), the response of the entanglement entropy is governed by the so-called “first law” of entanglement entropy, in which the change in entanglement entropy is proportional to the change in energy. Whether such a first law holds for other types of perturbations, such as a change to the CFT Lagrangian, remains an open question. We use holography to study the evolution in time t of entanglement entropy for a CFT driven by a t-linear source for a conserved U(1) current or marginal scalar operator. We find that although the usual first law of entanglement entropy may be violated, a first law for the rates of change of entanglement entropy and energy still holds. More generally, we prove that this first law for rates holds in holography for any asymptotically (d+1)-dimensional anti–de Sitter metric perturbation whose t dependence first appears at order zd in the Fefferman-Graham expansion about the boundary at z=0.

  • Received 6 July 2017

DOI:https://doi.org/10.1103/PhysRevD.96.066028

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Andy O’Bannon1,*, Jonas Probst2,†, Ronnie Rodgers1,‡, and Christoph F. Uhlemann3,4,§

  • 1STAG Research Centre, Physics and Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
  • 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
  • 3Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
  • 4Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA

  • *a.obannon@soton.ac.uk
  • Jonas.Probst@physics.ox.ac.uk
  • R.J.Rodgers@soton.ac.uk
  • §uhlemann@physics.ucla.edu

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Issue

Vol. 96, Iss. 6 — 15 September 2017

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