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 construct a replica technique to perturbatively compute the odd entanglement entropy (OEE) for bipartite mixed states in <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> deformed <math><mrow><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mi>s</mi></mrow></math>. This framework is then utilized to obtain the leading-order correction to the OEE for two disjoint intervals, two adjacent intervals, and a single interval in <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> deformed thermal <math><mrow><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mi>s</mi></mrow></math> in the large central charge limit. The field theory results are subsequently reproduced in the high-temperature limit from holographic computations for the entanglement wedge cross sections in the dual bulk finite cutoff Bañados-Teitelboim-Zanelli geometries. We further show that for finite size <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> deformed <math><mrow><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow><mi>s</mi></mrow></math> at zero temperature the corrections to the OEE are vanishing to the leading order from both field theory and bulk holographic computations.

Debarshi Basu

Saikat Biswas

Ankur Dey

Odd entanglement entropy in <math><mrow><mi>T</mi><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> deformed <math><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>s</mi></mrow></math> and holography

We obtain the entanglement negativity for various bipartite zero and finite temperature pure and mixed state configurations in a class of (<math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional Galilean conformal field theories. In this context, we establish a construction for computing the entanglement negativity for such bipartite states involving a suitable replica technique. Our construction exactly reproduces certain universal features observed for entanglement negativity of corresponding states in relativistic (<math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional conformal field theories.

Vinay Malvimat

Entanglement negativity in Galilean conformal field theories

We advance a construction for the covariant holographic entanglement negativity for time dependent mixed states of disjoint intervals in $$(1+1)$$ <math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math>  dimensional conformal field theories ($$CFT_{1+1}$$ <math><mrow><mi>C</mi><mi>F</mi><msub><mi>T</mi><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></msub></mrow></math> ) dual to bulk non static $$AdS_3$$ <math><mrow><mi>A</mi><mi>d</mi><msub><mi>S</mi><mn>3</mn></msub></mrow></math>  geometries. Application of our proposal to such mixed states in a $$CFT_{1+1}$$ <math><mrow><mi>C</mi><mi>F</mi><msub><mi>T</mi><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></msub></mrow></math>  dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduces the replica technique results in the large central charge limit. We also investigate the time dependent holographic entanglement negativity for such mixed states in a $$CFT_{1+1}$$ <math><mrow><mi>C</mi><mi>F</mi><msub><mi>T</mi><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></msub></mrow></math>  dual to a bulk Vaidya-$$AdS_3$$ <math><mrow><mi>A</mi><mi>d</mi><msub><mi>S</mi><mn>3</mn></msub></mrow></math>  geometry in the context of their thermalization involving bulk black hole formation.

Sayid Mondal

Covariant holographic entanglement negativity for disjoint intervals in $$AdS_3/CFT_2$$ <math><mrow><mi>A</mi><mi>d</mi><msub><mi>S</mi><mn>3</mn></msub><mo>/</mo><mi>C</mi><mi>F</mi><msub><mi>T</mi><mn>2</mn></msub></mrow></math>

We advance a holographic construction for the entanglement negativity of bipartite mixed state configurations of two disjoint intervals in $$(1+1)$$ <math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math>  dimensional conformal field theories ($$CFT_{1+1}$$ <math><mrow><mi>C</mi><mi>F</mi><msub><mi>T</mi><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></msub></mrow></math> ) through the $$AdS_3/CFT_2$$ <math><mrow><mi>A</mi><mi>d</mi><msub><mi>S</mi><mn>3</mn></msub><mo>/</mo><mi>C</mi><mi>F</mi><msub><mi>T</mi><mn>2</mn></msub></mrow></math>  correspondence. Our construction constitutes the large central charge analysis of the entanglement negativity for mixed states under consideration and involves a specific algebraic sum of bulk space like geodesics anchored on appropriate intervals in the dual $$CFT_{1+1}$$ <math><mrow><mi>C</mi><mi>F</mi><msub><mi>T</mi><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></msub></mrow></math> . The construction is utilized to compute the holographic entanglement negativity for such mixed states in $$CFT_{1+1}$$ <math><mrow><mi>C</mi><mi>F</mi><msub><mi>T</mi><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></msub></mrow></math> s dual to bulk pure $$AdS_3$$ <math><mrow><mi>A</mi><mi>d</mi><msub><mi>S</mi><mn>3</mn></msub></mrow></math>  geometries and BTZ black holes respectively. Our analysis exactly reproduces the universal features of corresponding replica technique results in the large central charge limit which serves as a consistency check.

Holographic entanglement negativity for disjoint intervals in $$AdS_3/CFT_2$$ <math><mrow><mi>A</mi><mi>d</mi><msub><mi>S</mi><mn>3</mn></msub><mo>/</mo><mi>C</mi><mi>F</mi><msub><mi>T</mi><mn>2</mn></msub></mrow></math>