Timelike Entanglement Entropy and Phase Transitions in non-Conformal Theories

We propose a holographic formalism for a timelike entanglement entropy in non-conformal theories. This pseudoentropy is a complex-valued measure of information, which, in holographic non-conformal theories, receives contributions from a set of spacelike surfaces and a finite timelike bulk surface with mirror symmetry. We suggest a method of merging the surfaces so that the boundary length of the subregion is exclusively specified by holography. We show that in confining theories, the surfaces can be merged in the bulk at the infrared tip of the geometry and are homologous to the boundary region. The timelike entanglement entropy receives its imaginary and real contributions from the timelike and the spacelike surfaces, respectively. Additionally, we demonstrate that in confining theories, there exists a critical length within which a connected non-trivial surface can exist, and the imaginary part of the timelike entanglement entropy is non-zero. Therefore, the timelike entanglement entropy exhibits unique behavior in confining theories, making it a probe of confinement and phase transitions. Finally, we discuss the entanglement entropy in Euclidean spacetime in confining theories and the effect of a simple analytical continuation from a spacelike subsystem to a timelike one.Comment: 1+32 pages, 5 figure

Holographic entanglement negativity for disjoint subsystems in AdSd+1/CFTd\mathrm{AdS_{d+1}/CFT_d}

We propose a construction to compute the holographic entanglement negativity for bipartite mixed state configurations of two disjoint subsystems (in proximity) in higher dimensional conformal field theories $(CFT_d)$ dual to bulk $AdS_{d+1}$ geometries. Our construction follows from the corresponding $AdS_3/CFT_2$ scenario and involves a specific algebraic sum of the areas of bulk co dimension two static minimal surfaces homologous to appropriate subsystems. Utilizing our construction we compute the holographic entanglement negativity for such bipartite mixed state configurations of two disjoint subsystems with long rectangular strip geometries in $CFT_d$s dual to bulk pure $AdS_{d+1}$ geometries and the $AdS_{d+1}$-Schwarzschild black holes.Comment: 20 pages, 5 figure

Reflected Entropy for Communicating Black Holes I: Karch-Randall Braneworlds

We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in $BCFT_2$s with two distinct boundaries through a replica technique in the large central charge limit. Subsequently these field theory results are reproduced from bulk computations involving the entanglement wedge cross section in the dual BTZ black hole geometry truncated by two Karch-Randall branes. Our result confirms the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the $AdS_3/BCFT_2$ scenario. We further investigate the critical issue of the holographic Markov gap between the reflected entropy and the mutual information for these configurations from the bulk braneworld geometry and study its variation with subsystem sizes and time.Comment: 68 pages, 42 figures, 2 appendice

On minimal entanglement wedge cross section for holographic entanglement negativity

We propose an alternate construction to compute the minimal entanglement wedge cross section (EWCS) for a single interval in a $(1+1)$ dimensional holographic conformal field theory at a finite temperature, dual to a bulk planar BTZ black hole geometry. Utilizing this construction we compute the holographic entanglement negativity for the above mixed state configuration from a recent conjecture in the literature. Our results exactly reproduce the corresponding replica technique results in the large central charge limit and resolves the issue of the missing thermal term for the holographic entanglement negativity computed earlier in the literature. In this context we compare the results for the holographic entanglement negativity utilizing the minimum EWCS and an alternate earlier proposal involving an algebraic sum of the lengths of the geodesics homologous to specific combinations of appropriate intervals. From our analysis we conclude that the two quantities are proportional in the context of the $AdS_3/CFT_2$ scenario and this possibly extends to the higher dimensional $AdS_{d+1}/CFT_d$ framework.Comment: 4 figures, 14 page

Holographic Reflected Entropy and Islands in Interface CFTs

We investigate the reflected entropy for various mixed state configurations in the two dimensional holographic conformal field theories sharing a common interface (ICFTs). In the AdS$_3$/ICFT$_2$ framework, we compute the holographic reflected entropy for the required configurations in the vacuum state of the ICFT$_{\text{2}}$ which is given by twice the entanglement wedge cross section (EWCS) in a spacetime involving two AdS$_3$ geometries glued along a thin interface brane. Subsequently, we evaluate the EWCS in the bulk geometry involving eternal BTZ black strings with an AdS$_2$ interface brane, which is dual to an ICFT$_2$ in the thermofield double (TFD) state. We explore the system from a doubly holographic perspective and determine the island contributions to the reflected entropy in the two dimensional semi-classical description involving two CFT$_{\text{2}}$s coupled to an AdS$_2$ brane. We demonstrate that the results from the island formula match precisely with the bulk AdS$_3$ results in the large tension limit of the interface brane. We illustrate that the phase structure of the reflected entropy is quite rich involving many novel induced island phases and demonstrate that it obeys the expected Page curve for the reflected entropy in a radiation bath coupled to the AdS$_2$ black hole.Comment: 68 pages, 28 figure

Holographic timelike entanglement entropy in non-relativistic theories

Abstract Timelike entanglement entropy is a complex measure of information that is holographically realized by an appropriate combination of spacelike and timelike extremal surfaces. This measure is highly sensitive to Lorentz invariance breaking. In this work, we study the timelike entanglement entropy in non-relativistic theories, focusing on theories with hyperscaling violation and Lifshitz-like spatial anisotropy. The properties of the extremal surfaces, as well as the timelike entanglement entropy itself, depend heavily on the symmetry-breaking parameters of the theory. Consequently, we show that timelike entanglement can encode, to a large extent, the stability and naturalness of the theory. Furthermore, we find that timelike entanglement entropy identifies Fermi surfaces either through the logarithmic behavior of its real part or, alternatively, via its constant imaginary part, with this constant value depending on the theory’s Lifshitz exponent. This provides a novel interpretation for the imaginary component of this pseudoentropy. Additionally, we examine temporal entanglement entropy, an extension of timelike entanglement entropy to Euclidean space, and provide a comprehensive discussion of its properties in these theories

Timelike entanglement entropy and phase transitions in non-conformal theories

Abstract We propose a holographic formalism for a timelike entanglement entropy in non-conformal theories. This pseudoentropy is a complex-valued measure of information, which, in holographic non-conformal theories, receives contributions from a set of spacelike surfaces and a finite timelike bulk surface with mirror symmetry. We suggest a method of merging the surfaces so that the boundary length of the subregion is exclusively specified by holography. We show that in confining theories, the surfaces can be merged in the bulk at the infrared tip of the geometry and are homologous to the boundary region. The timelike entanglement entropy receives its imaginary and real contributions from the timelike and the spacelike surfaces, respectively. Additionally, we demonstrate that in confining theories, there exists a critical length within which a connected non-trivial surface can exist, and the imaginary part of the timelike entanglement entropy is non-zero. Therefore, the timelike entanglement entropy exhibits unique behavior in confining theories, making it a probe of confinement and phase transitions. Finally, we discuss the entanglement entropy in Euclidean spacetime in confining theories and the effect of a simple analytical continuation from a spacelike subsystem to a timelike one

Reflected entropy for communicating black holes II: Planck braneworlds

We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in finite-sized non-gravitating reservoirs described by $$CFT_2$$s each coupled to two quantum dots at their boundaries in the large central charge limit through a replica technique. These field theory results are substantiated through a holographic computation involving the entanglement wedge cross section in the dual bulk BTZ black hole geometry truncated by two Planck branes. The two Planck branes are the holographic duals of the quantum dots described by $$AdS_2$$ slices with JT black holes. Our result reproduce the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the $$AdS_3/CFT_2$$ correspondence. Subsequently we analyze the behaviour of the holographic Markov gap between the reflected entropy and the mutual information for different scenarios involving the subsystem sizes and time