Universal Bound on Effective Central Charge and Its Saturation.

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• String Theory

Background:

• Conformal interfaces are crucial in understanding entanglement and energy flow in quantum systems.
• The effective central charge (c_eff) quantifies entanglement, while the transmission coefficient (c_LR) measures energy transmission, and they are known to differ.

Purpose of the Study:

• To establish fundamental inequalities relating entanglement and energy transmission across conformal interfaces.
• To demonstrate that energy transmission is bounded by entanglement, i.e., 0≤c_LR≤c_eff≤min(c_L,c_R).

Main Methods:

• Derivation of inequalities using theoretical physics principles.
• Verification through the AdS/CFT correspondence.
• Application of perturbation methods.
• Analysis of examples beyond holographic duality.

Main Results:

• Proposed and proved the inequalities 0≤c_LR≤c_eff≤min(c_L,c_R).
• Demonstrated that energy transmission (c_LR) cannot exceed entanglement (c_eff).
• Confirmed the sharpness of these inequalities by constructing saturating interface examples.

Conclusions:

• The established inequalities provide a fundamental constraint on energy and entanglement flow across conformal interfaces.
• These findings have broad implications for quantum information theory and condensed matter physics.
• The universality of the inequalities is supported by diverse verification methods.