TY - JOUR

T1 - Linearity of holographic entanglement entropy

AU - Almheiri, Ahmed

AU - Dong, Xi

AU - Swingle, Brian

N1 - Publisher Copyright:
© 2017, The Author(s).

PY - 2017/2/1

Y1 - 2017/2/1

N2 - We consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of ‘entropy operators’ in general systems with a large number of degrees of freedom.

AB - We consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of ‘entropy operators’ in general systems with a large number of degrees of freedom.

KW - AdS-CFT Correspondence

KW - Black Holes in String Theory

KW - Conformal Field Theory

KW - Gauge-gravity correspondence

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U2 - 10.1007/JHEP02(2017)074

DO - 10.1007/JHEP02(2017)074

M3 - Article

AN - SCOPUS:85013057087

SN - 1126-6708

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 2

M1 - 74

ER -