We propose a covariant holographic construction based on the extremal entanglement wedge cross section, for the entanglement negativity of bipartite states in <math altimg='si1.svg'><mi>C</mi><mi>F</mi><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>1</mn></mrow></msub></math>s dual to non static bulk <math altimg='si2.svg'><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math> geometries. Utilizing our proposal we obtain the holographic entanglement negativity for bipartite mixed states in <math altimg='si1.svg'><mi>C</mi><mi>F</mi><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>1</mn></mrow></msub></math>s dual to bulk extremal and non extremal rotating BTZ black holes and the time dependent Vaidya- <math altimg='si2.svg'><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math> geometries. Our results correctly reproduce the replica technique results modulo certain constants for the corresponding dual <math altimg='si1.svg'><mi>C</mi><mi>F</mi><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>1</mn></mrow></msub></math>s in the large central charge limit for the bulk black hole geometries. Furthermore for all the cases our results also match upto such constants with the corresponding results from an earlier alternate covariant holographic construction in the literature. This demonstrates the equivalence modulo constants of the two constructions for the <math altimg='si3.svg'><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub><mo stretchy='false'>/</mo><mi>C</mi><mi>F</mi><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub></math> scenario.

India

Jaydeep Kumar Basak

Himanshu Parihar

Boudhayan Paul

Gautam Sengupta

Covariant holographic negativity from the entanglement wedge in AdS <inf>3</inf>/CFT <inf>2</inf>

We obtain the holographic entanglement negativity for bipartite mixed states at a finite temperature in baths described by conformal field theories dual to configurations involving two communicating black holes in a braneworld geometry. In this context, we analyze the mixed state entanglement structure characterized by the information transfer between the black holes. The model corresponds to a configuration of two dimensional eternal Jackiw-Teitelboim (JT) black holes in a braneworld geometry involving two Planck branes coupled through shared bath systems described by <math><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>s</mi></mrow></math>. Our results reproduce analogue of the Page curves for the entanglement negativity obtained earlier in the context of random matrix theory and from geometric evaporation in JT black hole configurations.