Nonlinear gravity from entanglement in conformal field theories
Abstract
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 ballshaped regions can always be represented geometrically (via the RyuTakayanagi 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 August 2017
 DOI:
 10.1007/JHEP08(2017)057
 arXiv:
 arXiv:1705.03026
 Bibcode:
 2017JHEP...08..057F
 Keywords:

 AdSCFT Correspondence;
 Conformal Field Theory;
 Classical Theories of Gravity;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 55 pages, 8 figures