We consider holographic entanglement entropy in AdS black hole backgrounds by using the limit of large number of dimensions. By dividing the geometry to two patches (with one patch covering the vicinity of the black hole horizon and another covering the other regions), we are able to obtain fully analytic expressions for the entropy when the entanglement region is a strip. We argue that apart from conformal field theories at finite temperature in high number of dimensions, our method works for nearly critical theories in 3+1 dimensions. In the case of extremal black holes, dual to quantum critical systems, the results take a particularly simple form. We also comment on the case of soliton geometries. Finally, we analyze entanglement entropy for wide strips, and propose a general formula for the first subleading term in the expansion of the entropy in (inverse) system size for generic entanglement regions.

India

Parul Jain

China

South Korea

Matti Järvinen

An analytic approach for holographic entanglement entropy at (quantum) criticality

We compute the entanglement entropy of Hawking radiation in a bath attached to a deformed eternal AdS black hole. This black hole is dual to the two identical strongly coupled large- <math altimg='si1.svg'><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></math> thermal field theories, where each theory is backreacted (deformed) by the presence of a uniform static distribution of heavy fundamental quarks. In our observation we find that the entanglement entropy of Hawking radiation increases in a quadratic manner for an early time and linearly for the late time. The large time expression for the entanglement entropy of Hawking radiation is used to find the Page curve and Page time. After the Page time, the entanglement entropy saturates to a constant value due to the appearance of an island. We observe that introducing deformation (backreaction) delays the appearance of island and shifts the Page curve to a later time. Subsequently, the computation of the scrambling time reveals an increase with the backreaction parameter, suggesting a longer duration for information retrieval in the presence of deformation. Moreover, our analysis of the mutual information between the radiation subsystems shows that it vanishes at a critical time which increases with the deformation before the Page time. After the Page time, the appearance of island leads to the vanishing of mutual information between black hole subsystems and gives the time difference of the order of scrambling time.

Sanjay Pant

Taiwan

Himanshu Parihar

Effect of backreaction on island, Page curve and mutual information

We study various holographic pure and mixed-state entanglement measures in the confined/deconfined phases of a bottom-up <math><mrow><mi>AdS</mi><mo>/</mo><mi>QCD</mi></mrow></math> model in the presence of a background magnetic field. We analyze the entanglement entropy, entanglement wedge cross section, mutual information, and entanglement negativity and investigate how a background magnetic field leaves its imprints on the entanglement structure of these measures. Due to the anisotropy introduced by the magnetic field, we find that the behavior of these measures depends nontrivially on the relative orientation of the strip with respect to the field. In the confining phase, the entanglement entropy and negativity undergo a phase transition at the same critical strip length, the magnitude of which increases/decreases for parallel/perpendicular orientation of the magnetic field. The entanglement wedge cross section similarly displays discontinuous behavior each time a phase transition between different entangling surfaces occurs, while further exhibiting anisotropic features with a magnetic field. We further find that the magnetic field also introduces substantial changes in the entanglement measures of the deconfined phase; however, these changes remain qualitatively similar for all orientations of the magnetic field. We further study the inequality involving the entanglement wedge and mutual information and find that the former always exceeds half of the latter everywhere in the parameter space of the confined/deconfined phases.

Siddhi Swarupa Jena

Subhash Mahapatra

Holographic confining-deconfining gauge theories and entanglement measures with a magnetic field

The entanglement wedge cross sections (EWCSs) are postulated as dual gravity probes to certain measures for the entanglement of multiparty systems. We test various proposed inequalities for EWCSs. As it turns out, contrary to expectations, the EWCS is not clearly monogamous nor polygamous for tripartite systems but the results depend on the details and dimensionality of the geometry of the gravity solutions. We propose weaker monogamy relations for dual entanglement measures, which lead to a new lower bound on EWCS. Our work is based on a plethora of gravity backgrounds: pure anti de Sitter spaces, anti de Sitter black branes, those induced by a stack of Dp-branes, and cigar geometries in generic dimension.

Finland

Niko Jokela

Bounding entanglement wedge cross sections

We study three different measures of quantum correlations—entanglement spectrum, entanglement entropy, and logarithmic negativity—for a (<math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional massive scalar field in a flat space-time. The entanglement spectrum for the discretized scalar field in the ground state indicates a crossover in the zero-mode regime, which is further substantiated by an analytical treatment of both entanglement entropy and logarithmic negativity. The exact nature of this crossover depends on the boundary conditions used—the leading order term switches from a log to log-log behavior for the periodic and Neumann boundary conditions. In contrast, for Dirichlet, it is the parameters within the leading log-log term that are switched. We show that this crossover manifests as a change in the behavior of the leading order divergent term for entanglement entropy and logarithmic negativity close to the zero-mode limit. We thus show that the two regimes have fundamentally different information content. Furthermore, an analysis of the ground-state fidelity shows us that the region between critical point <math><mi>Λ</mi><mo>=</mo><mn>0</mn></math> and the crossover point is dominated by zero-mode effects, featuring an explicit dependence on the IR cutoff of the system. For the reduced state of a single oscillator, we show that this crossover occurs in the region <math><mi>N</mi><mi>a</mi><msub><mi>m</mi><mi>f</mi></msub><mo>∼</mo><mi>𝒪</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>.

S. Mahesh Chandran

S. Shankaranarayanan

Log to log-log crossover of entanglement in a <math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math>-dimensional massive scalar field

We study holographic aspects of mixed state entanglement measures in various large <math><mi>N</mi></math> top-down as well as bottom-up confining models. For the top-down models, we consider wrapped <math><mi>D</mi><mn>3</mn></math> and <math><mi>D</mi><mn>4</mn></math> brane gravity solutions, whereas, for the bottom-up confining model, the Einstein-Maxwell-dilaton gravity solution is considered. We study entanglement entropy, mutual information, entanglement wedge cross section, and entanglement negativity for the strip subsystems and find model-independent features of these entanglement measures in all confining theories. The entanglement negativity and entropy exhibit a phase transition at the same critical strip length <math><msub><mi>L</mi><mrow><mi>crit</mi></mrow></msub></math>, at which the order of these measures changes from <math><mi>O</mi><mo>(</mo><msup><mi>N</mi><mn>2</mn></msup><mo>)</mo></math> to <math><mi>O</mi><mo>(</mo><msup><mi>N</mi><mn>0</mn></msup><mo>)</mo></math>. The entanglement wedge cross section similarly shows an order change at <math><msub><mi>L</mi><mrow><mi>crit</mi></mrow></msub></math> and exhibits a discontinuous behavior each time a phase transition between different entangling surfaces occurs. We further test the inequality involving mutual information and entanglement wedge cross section and find that the latter always exceeds half of the former.

Mixed state entanglement measures as probe for confinement

We propose a holographic entanglement negativity conjecture involving the bulk geometry, for mixed states of adjacent intervals in <math><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></math>-dimensional dual conformal field theories through the <math><mi>A</mi><mi>d</mi><mi>S</mi><mo>/</mo><mi>C</mi><mi>F</mi><mi>T</mi></math> correspondence. The holographic entanglement negativity is obtained from a specific algebraic sum of the geodesics anchored on respective intervals on the boundary which reduces to the holographic mutual information between them. Utilizing our conjecture we obtain the entanglement negativity of adjacent intervals in zero and finite temperature (<math><mn>1</mn><mo>+</mo><mn>1</mn></math>)-dimensional holographic conformal field theories dual to the bulk <math><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math> vacuum and the Euclidean BTZ black hole respectively. Our holographic conjecture exactly reproduces the conformal field theory results obtained through the replica technique, in the large central charge limit. We briefly elucidate the corresponding issue for the <math><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>/</mo><mi>C</mi><mi>F</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>d</mi></mrow></msub></math> scenario.

Italy

Vinay Malvimat

Sayid Mondal

Gautam Sengupta

Holographic entanglement negativity conjecture for adjacent intervals in AdS /cft

We propose a covariant holographic entanglement negativity construction for time dependent mixed states of adjacent intervals in <math><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></math>-dimensional conformal field theories dual to non-static bulk <math><mi>Ad</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math> configurations. Our prescription applied to <math><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></math>-dimensional conformal field theories with a conserved charge dual to non-extremal and extremal rotating BTZ black holes exactly reproduces the corresponding replica technique results, in the large central charge limit. We also utilize our construction to obtain the time dependent holographic entanglement negativity for the mixed state in question for the <math><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></math>-dimensional CFT dual to a bulk Vaidya-<math><mi>Ad</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math> configuration.

Covariant holographic entanglement negativity for adjacent subsystems in AdS /cft

We study the application of our recent holographic entanglement negativity conjecture for mixed states of adjacent subsystems in conformal field theories with a conserved charge. In this context we obtain the holographic entanglement negativity for zero and finite temperature mixed state configurations in d-dimensional conformal field theories dual to bulk extremal and non extremal charged $$AdS_{d+1}$$ <math><mrow><mi>A</mi><mi>d</mi><msub><mi>S</mi><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math>  black holes. Our results conform to quantum information theory expectations and constitute significant consistency checks for our conjecture.