Action and entanglement in gravity and field theory

Area of Science:

• Theoretical physics
• Quantum gravity
• Quantum field theory

Background:

• Entanglement entropy in quantum field theory relies on short-distance regularization.
• Quantum gravity is expected to bypass this regularization.
• A conjecture posits that quantum gravity's entanglement entropy matches black hole entropy formulas.

Purpose of the Study:

• To investigate the classical action counterparts of statements regarding entanglement entropy in quantum gravity.
• To explore the role of nonadditive imaginary parts in classical actions.

Main Methods:

• Analysis of classical actions in gravitational and nongravitational theories.
• Examination of the nonadditive imaginary part of the action.
• Heuristic application of the action-wave function relation.

Main Results:

• Precise classical counterparts to quantum gravity entanglement entropy statements were identified at the action level.
• The nonadditive imaginary part of the action is fixed by the black hole entropy formula in gravity.
• In nongravitating theories, this imaginary part is arbitrary.

Conclusions:

• The entanglement entropy conjecture in quantum gravity is supported by classical action properties.
• Classical actions provide a foundation for understanding entanglement entropy in quantum gravity.
• The black hole entropy formula plays a crucial role in fixing the action's imaginary part in gravitational theories.