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Entanglement entropy from one-point functions in holographic states

Matthew J.S. Beach
(
- British Columbia U.
)
,
Jaehoon Lee
(
- British Columbia U.
)
,
Charles Rabideau
(
- British Columbia U.
)
,
Mark Van Raamsdonk
(
- British Columbia U.
)

Apr 18, 2016

32 pages

Published in:

JHEP 06 (2016) 085

Published: Jun 15, 2016

e-Print:

1604.05308 [hep-th]

DOI:

10.1007/JHEP06(2016)085

View in:

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Abstract: (Springer)

For holographic CFT states near the vacuum, entanglement entropies for spatial subsystems can be expressed perturbatively as an expansion in the one-point functions of local operators dual to light bulk fields. Using the connection between quantum Fisher information for CFT states and canonical energy for the dual spacetimes, we describe a general formula for this expansion up to second-order in the one-point functions, for an arbitrary ball-shaped region, extending the first-order result given by the entanglement first law. For two-dimensional CFTs, we use this to derive a completely explicit formula for the second-order contribution to the entanglement entropy from the stress tensor. We show that this stress tensor formula can be reproduced by a direct CFT calculation for states related to the vacuum by a local conformal transformation. This result can also be reproduced via the perturbative solution to a non-linear scalar wave equation on an auxiliary de Sitter spacetime, extending the first-order result in arXiv:1509.00113 .

Note:

34 pages, 2 figures; v2 references added, minor typos corrected

AdS-CFT Correspondence
Gauge-gravity correspondence
entropy: entanglement
transformation: conformal
space-time: de Sitter
operator: local
duality: holography
nonlinear
field theory: conformal
n-point function: 1

References(34)

Figures(2)

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