Higher Curvature Gravity from Entanglement in Conformal Field Theories

Area of Science:

• Theoretical Physics
• Quantum Gravity
• String Theory

Background:

• Entanglement entropy calculations in conformal field theories (CFTs) are often linked to spacetime geometry via the Ryu-Takayanagi formula.
• Higher curvature gravity theories introduce complexities beyond Einstein-Hilbert gravity.
• Previous work established connections between CFT properties and gravitational duals, but a unified framework was lacking.

Purpose of the Study:

• To develop a unifying framework for entanglement entropy and relative entropy in higher curvature gravity.
• To generalize existing results to higher curvature regimes.
• To provide novel derivations for holographic duals of CFT quantities.

Main Methods:

• Generalization of recent works on entanglement entropy to higher curvature gravity.
• Application of a generalized Ryu-Takayanagi formula.
• Derivation of holographic duals for entanglement entropy and relative entropy.

Main Results:

• A unified framework for three related results in higher curvature gravity.
• Confirmation that asymptotically anti-de Sitter (AdS) spacetimes satisfying specific conditions compute entanglement entropies up to second order.
• The holographic dual of entanglement entropy in higher curvature gravity is Wald entropy plus an extrinsic curvature correction, derived without the replica trick.
• Conformal field theory relative entropy is dual to gravitational canonical energy.

Conclusions:

• The study provides a consistent framework linking CFT observables to gravitational dynamics in higher curvature theories.
• The novel derivation of the entanglement entropy dual avoids the Euclidean replica trick, offering a new perspective.
• The results deepen the understanding of the holographic principle in more general gravitational theories.