Derivation of Holographic Negativity in AdS_{3}/CFT_{2}

Area of Science:

• Quantum Gravity
• String Theory
• Condensed Matter Physics

Background:

• The holographic principle connects gravity theories to quantum field theories.
• Logarithmic negativity is a measure of quantum entanglement.
• AdS_{3}/CFT_{2} provides a tractable model for studying quantum gravity and entanglement.

Purpose of the Study:

• To derive the holographic dual of logarithmic negativity in AdS_{3}/CFT_{2}.
• To connect geometric concepts (extremal cosmic brane area) with quantum information measures (logarithmic negativity).
• To clarify aspects of negativity in conformal field theories with large central charge.

Main Methods:

• Relating Rényi reflected entropy to logarithmic negativity.
• Utilizing the framework of holographic conformal field theories.
• Investigating properties of conformal blocks.

Main Results:

• A geometric interpretation of logarithmic negativity as the area of an extremal cosmic brane.
• Successful derivation of the holographic dual for logarithmic negativity in AdS_{3}/CFT_{2}.
• Clarification of previously enigmatic features of negativity at large central charge.

Conclusions:

• The area of an extremal cosmic brane is the holographic dual of logarithmic negativity in AdS_{3}/CFT_{2}.
• The study provides a concrete link between geometry and entanglement in holographic settings.
• Future work can explore generalizations to higher dimensions and dynamical scenarios.