SciPost Phys. 5, 060 (2018) ·
published 10 December 2018

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We investigate the existence of a stateoperator correspondence on the torus.
This correspondence would relate states of the CFT Hilbert space living on a
spatial torus to the path integral over compact Euclidean manifolds with
operator insertions. Unlike the states on the sphere that are associated to
local operators, we argue that those on the torus would more naturally be
associated to line operators. We find evidence that such a correspondence
cannot exist and in particular, we argue that no compact Euclidean path
integral can produce the vacuum on the torus. Our arguments come solely from
field theory and formulate a CFT version of the HorowitzMyers conjecture for
the AdS soliton.
SciPost Phys. 5, 024 (2018) ·
published 20 September 2018

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We compute the bulk entanglement entropy across the RyuTakayanagi surface
for a oneparticle state in a scalar field theory in AdS$_3$. We work directly
within the bulk Hilbert space and include the spatial spread of the scalar
wavefunction. We give closed form expressions in the limit of small interval
sizes and compare the result to a CFT computation of entanglement entropy in an
excited primary state at large $c$. Including the contribution from the
backreacted minimal area, we find agreement between the CFT result and the FLM
and JLMS formulas for quantum corrections to holographic entanglement entropy.
This provides a nontrivial check in a state where the answer is not dictated
by symmetry. Along the way, we provide closedform expressions for the scalar
field Bogoliubov coefficients that relate the global and Rindler slicings of
AdS$_3$.