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arXiv:1312.2839 · Journal of High Energy Physics

Entanglement and correlations near extremality: CFTs dual to Reissner-Nordström AdS5

Tomás Andrade, Sebastian Fischetti, Donald M. Marolf, Simon F. Ross, Moshe Rozali A

Published Apr 1, 2014• 24 citations

Abstract

We use the AdS/CFT correspondence to study models of entanglement and correlations between two d = 4 CFTs in thermofield double states at finite chemical potential. Our bulk spacetimes are planar Reissner-Nordström AdS black holes. We compute both thermo-mutual information and the two-point correlators of large-dimension scalar operators, focussing on the small-temperature behavior — an infrared limit with behavior similar to that seen at large times. The interesting feature of this model is of course that the entropy density remains finite as T → 0 while the bulk geometry develops an infinite throat. This leads to a logarithmic divergence in the scale required for non-zero mutual information between equal-sized strips in the two CFTs, though the mutual information between one entire CFT and a finite-sized strip in the other can remain non-zero even at T =0. Furthermore,despitetheinfinitethroat,therecanbeextremallychargedoperators for which the two-point correlations remain finite as T → 0. This suggests an interestingly mixed picture in which some aspects of the entanglement remain localized on scales set by the chemical potential, while others shift to larger and larger scales. We also comment on implications for the localized-quasiparticle picture of entanglement.

DOI: 10.1007/jhep04(2014)023

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We use the AdS/CFT correspondence to study models of entanglement and correlations between two d = 4 CFTs in thermofield double states at finite chemical potential. Our bulk spacetimes are planar Reissner-Nordström AdS black holes. We compute both thermo-mutual information and the two-point correlators of large-dimension scalar operators, focussing on the small-temperature behavior — an infrared limit with behavior similar to that seen at large times. The interesting feature of this model is of course that the entropy density remains finite as T → 0 while the bulk geometry develops an infinite throat. This leads to a logarithmic divergence in the scale required for non-zero mutual information between equal-sized strips in the two CFTs, though the mutual information between one entire CFT and a finite-sized strip in the other can remain non-zero even at T =0. Furthermore,despitetheinfinitethroat,therecanbeextremallychargedoperators for which the two-point correlations remain finite as T → 0. This suggests an interestingly mixed picture in which some aspects of the entanglement remain localized on scales set by the chemical potential, while others shift to larger and larger scales. We also comment on implications for the localized-quasiparticle picture of entanglement.

We study entanglement in thermofield double states of strongly coupled conformal field theories by analyzing two-sided Reissner-Nordstr\"om solutions in anti--de Sitter space. The central object of study is the mutual information between a pair of regions, one on each asymptotic boundary of the black hole. For large regions the mutual information is positive and for small ones it vanishes; we compute the critical length scale, which goes to infinity for extremal black holes, of the transition. We also generalize the butterfly effect of Shenker and Stanford [J. High Energy Phys. 03 (2014) 067] to a wide class of charged black holes, showing that mutual information is disrupted upon perturbing the system and waiting for a time of order $\mathrm{log}E/\ensuremath{\delta}E$ in units of the temperature. We conjecture that the parametric form of this time scale is universal.

A standard insight of the AdS/CFT correspondence is that some aspects of the geometry of a bulk state are encoded in the entanglement structure of its dual boundary state. As entanglement is not a linear quantum observable, this means that geometry in a quantum theory of gravity should likewise not be a linear observable. This allows for linear dependencies between states with distinct geometries. We explore linear dependencies between certain states with simple geometric duals: states made up of

n

copies of a thermofield double state and the states obtained from this one by permuting the

n

right hand sides. There are

n!

such states, all dual to distinct geometries. We derive expressions for the maximum fidelity between one such state and a linear combination of the others, and see that this fidelity approaches 1 as the number

n

of black holes increases. We also consider the possibility of obtaining a single thermofield double state as the partial trace of a superposition of states whose topology does not connect the two untraced sides. We derive lower bounds for the fidelity between the thermofield double state and such partial traces and comment on the conceptual implications of the existence of such states.

Abstract In this paper, we consider the evolution of the thermofield-double state under the double-traced operator that connects its both sides. We will compute the entanglement entropy of the resulting state using the replica trick for the large N field theory. To leading order, it can be computed from the two-point function of the theory, where, in CFTs, it is fixed by the symmetries. Due to the exponential decay of the interaction, the entanglement entropy saturates about the thermal time after the interaction is on. Next, we restrict ourselves to one dimension and assume that the theory at strong coupling is effectively described by the Schwarzian action. We then compute the coarse-grained entropy of the resulting state using the four-point function. The equality of the two entropies implies that the double-traced operators in our theory act coherently. In AdS/CFT correspondence where the thermofield-double state corresponds to a two-sided black hole, the action of a double-traced operator corresponds to shrinking or expanding the black hole in the bulk.

Abstract We extend the results of arXiv:2209.12903 by studying local projective measurements performed on subregions of two copies of a CFT2 in the thermofield double state and investigating their consequences on the bulk double-sided black hole holographic dual. We focus on CFTs defined on an infinite line and consider measurements of both finite and semi-infinite subregions. In the former case, the connectivity of the bulk spacetime is preserved after the measurement. In the latter case, the measurement of two semi-infinite intervals in one CFT or of one semi-infinite interval in each CFT can destroy the Einstein-Rosen bridge and disconnect the bulk dual spacetime. In particular, we find that a transition between a connected and disconnected phase occurs depending on the relative size of the measured and unmeasured subregions and on the specific Cardy state the measured subregions are projected on. We identify this phase transition as an entangled/disentangled phase transition of the dual CFT system by computing the post-measurement holographic entanglement entropy between the two CFTs. We also find that bulk information encoded in one CFT in the absence of measurement can sometimes be reconstructed from the other CFT when a measurement is performed, or can be erased by the measurement. Finally, we show that a purely CFT calculation of the Renyi entropy using the replica trick yields results compatible with those obtained in our bulk analysis.

Abstract Recently, it was proposed that a

T\overline{T}

T T ¯ deformed CFT is dual to a gravity theory in an asymptotically AdS spacetime at finite radial cutoff. Motivated by this proposal, we explore some aspects of Hyperscaling Violating geometries at finite cutoff and zero temperature. We study holographic entanglement entropy, mutual information (HMI) and entanglement wedge cross section (EWCS) for entangling regions in the shape of strips. It is observed that the HMI shows interesting features in comparison to the very small cutoff case: it is a decreasing function of the cutoff. It is finite when the distance between the two entangling regions goes to zero. The location of its phase transition also depends on the cutoff, and decreases by increasing the cutoff. On the other hand, the EWCS is a decreasing function of the cutoff. It does not show a discontinuous phase transition when the HMI undergoes a first-order phase transition. However, its concavity changes. Moreover, it is finite when the distance between the two strips goes to zero. Furthermore, it satisfies the bound EW ≥

\frac{I}{2}

I 2 for all values of the cutoff.