Abstract In this paper, we study a holographic description of weak measurements in conformal field theories (CFTs). Weak measurements can be viewed as a soft projection that interpolates between an identity operator and a projection operator, and can induce an effective central charge distinct from the unmeasured CFT. We model the weak measurement by an interface brane, separating different geometries dual to the post-measurement state and the unmeasured CFT, respectively. In an infinite system, the weak measurement is related to ICFT via a spacetime rotation. We find that the holographic entanglement entropy with twist operators located on the defect is consistent in both calculations for ICFT and weak measurements. We additionally calculate the boundary entropy via holographic entanglement as well as partition function. In a finite system, the weak measurement can lead to a rich phase diagram: for marginal measurements the emergent brane separates two AdS geometries, while for irrelevant measurements the post-measurement geometry features an AdS spacetime and a black hole spacetime that are separated by the brane. Although the measurement is irrelevant in the later phase, the post-measurement geometry can realize a Python’s lunch. Finally, we discuss the thick brane construction for measurement and higher-dimension extensions of our model. For these general cases, our results above are still shown to be valid.
Abstract In this paper, we study a holographic description of weak measurements in conformal field theories (CFTs). Weak measurements can be viewed as a soft projection that interpolates between an identity operator and a projection operator, and can induce an effective central charge distinct from the unmeasured CFT. We model the weak measurement by an interface brane, separating different geometries dual to the post-measurement state and the unmeasured CFT, respectively. In an infinite system, the weak measurement is related to ICFT via a spacetime rotation. We find that the holographic entanglement entropy with twist operators located on the defect is consistent in both calculations for ICFT and weak measurements. We additionally calculate the boundary entropy via holographic entanglement as well as partition function. In a finite system, the weak measurement can lead to a rich phase diagram: for marginal measurements the emergent brane separates two AdS geometries, while for irrelevant measurements the post-measurement geometry features an AdS spacetime and a black hole spacetime that are separated by the brane. Although the measurement is irrelevant in the later phase, the post-measurement geometry can realize a Python’s lunch. Finally, we discuss the thick brane construction for measurement and higher-dimension extensions of our model. For these general cases, our results above are still shown to be valid.
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 Holography has taught us that spacetime is emergent and its properties depend on the entanglement structure of the dual theory. In this paper, we describe how changes in the entanglement due to a local projective measurement (LPM) on a subregion A of the boundary theory modify the bulk dual spacetime. We find that LPMs destroy portions of the bulk geometry, yielding post-measurement bulk spacetimes dual to the complementary unmeasured region Ac that are cut off by end-of-the-world branes. Using a bulk calculation in AdS3 and tensor network models of holography (in particular, the HaPPY code and random tensor networks), we show that the portions of the bulk geometry that are preserved after the measurement depend on the size of A and the state we project onto. The post-measurement bulk dual to Ac includes regions that were originally part of the entanglement wedge of A prior to measurement. This suggests that LPMs performed on a boundary subregion A teleport part of the bulk information originally encoded in A into the complementary region Ac. In semiclassical holography an arbitrary amount of bulk information can be teleported in this way, while in tensor network models the teleported information is upper-bounded by the amount of entanglement shared between A and Ac due to finite-N effects. When A is the union of two disjoint subregions, the measurement triggers an entangled/disentangled phase transition between the remaining two unmeasured subregions, corresponding to a connected/disconnected phase transition in the bulk description. Our results shed new light on the effects of measurement on the entanglement structure of holographic theories and give insight on how bulk information can be manipulated from the boundary theory. They could also represent a first step towards a holographic description of measurement-induced phase transitions.
Entanglement entropy in holographic conformal field theories with boundaries of generic spacetime signature cannot be described entirely within the standard holographic duality to a real bulk spacetime. We show, both in static and time-dependent setups, that an exact match with the conformal field theory predictions in two boundary dimensions entails an extension of the dual spacetime to complex coordinates. As a consequence, relevant bulk objects such as Ryu-Takayanagi surfaces and branes are in general complex, yet anchored on a real asymptotic boundary preserving the physical meaning of field-theoretical quantities. We also provide a third numerical check of the holographic prediction with a two-dimensional system of free Gaussian fermions exhibiting the same asymptotic regimes across different entanglement phases.
We study holographic entanglement entropy in 3-dimensional AdS gravity with conformal boundary conditions which fix the conformal class of the boundary metric and its extrinsic curvature, K, while leaving the Weyl mode dynamical. Extending Lewkowycz-Maldacena-Dong's replica construction, we derive the corresponding holographic entanglement entropy formula. We show that the fluctuating Weyl mode does not contribute additional entropy. The entropy of the full boundary is therefore the Bekenstein-Hawking entropy, and the entropy of a boundary subregion continues to obey the Ryu-Takayanagi prescription, namely, the area of a minimal surface divided by 4GN. We carry out explicit calculations for global AdS, rotating and non-rotating BTZ geometries. For an interval in AdS3 we find that the K-dependent holographic entanglement entropy is governed by cm=2GN3ℓ. For a thermal state at high conformal temperatures we find that, the entropy is governed by ceff=2GN3ℓ2Kℓ−K2ℓ2−4, the same effective central charge that governs the Cardy-like density of states, in agreement with previous results in the literature. Finally, we also compute the entanglement entropy directly from the conjectured dual boundary theory - a holographic CFT coupled with time-like Liouville theory and deformed by a marginal TTˉ like operator - and find SEE=3ceffln(ε2Rsinϕ0). This result for the state with no operator insertions (vacuum state ), provides an independent boundary realization of ceff while clarifying that this state is not the state dual to global AdS.
We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that these individual microstates of holographic CFTs effectively thermalize at the level of the single-interval entanglement entropy. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.
Holographic Entanglement Entropy in Janus deformed AdS3 Geometries
We investigate the time dependent entanglement entropy for boosted single intervals in interface conformal field theories (ICFT2s) dual to Janus deformed AdS3 geometries. For a Janus deformed Poincaré AdS3 background, we obtain the entanglement entropy and a Janus induced correction using a replica technique for the equivalent dual field theory described on a conformally flat background on corresponding AdS2 slices on the asymptotic boundary. The holographic entanglement entropy is then computed through certain embedding relations for the bulk Janus deformed AdS3 geometry which exactly match with the field theory results. We further extend our analysis to investigate the entanglement entropy of corresponding intervals in ICFT2s dual to bulk Janus deformed BTZ black hole and AdS3 black string geometries obtaining consistent results from both the field theoretic and bulk computations.