Nonlinear gravity from entanglement in conformal field theories

Thomas Faulkner, Felix M. Haehl, Eliot Hijano, Onkar Parrikar, Charles Rabideau, Mark Van Raamsdonk

Research output: Contribution to journalArticlepeer-review


In this paper, we demonstrate the emergence of nonlinear gravitational equations directly from the physics of a broad class of conformal field theories. We consider CFT excited states defined by adding sources for scalar primary or stress tensor operators to the Euclidean path integral defining the vacuum state. For these states, we show that up to second order in the sources, the entanglement entropy for all ball-shaped regions can always be represented geometrically (via the Ryu-Takayanagi formula) by an asymptotically AdS geometry. We show that such a geometry necessarily satisfies Einstein’s equations perturbatively up to second order, with a stress energy tensor arising from matter fields associated with the sourced primary operators. We make no assumptions about AdS/CFT duality, so our work serves as both a consistency check for the AdS/CFT correspondence and a direct demonstration that spacetime and gravitational physics can emerge from the description of entanglement in conformal field theories.

Original languageEnglish (US)
Article number57
JournalJournal of High Energy Physics
Issue number8
StatePublished - Aug 1 2017


  • AdS-CFT Correspondence
  • Classical Theories of Gravity
  • Conformal Field Theory

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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