Universal Bound on Effective Central Charge and Its Saturation

The effective central charge (denoted by c eff ) is a measure of entanglement through a conformal interface, while the transmission coefficient (encoded in the coefficient c LR of the two-point function of the energy-momentum tensor across the interface) is a measure of energy transmission through the interface. It has been pointed out that these two are generally different. In this Letter, we propose the inequalities, 0 <= c LR <= c eff <= min & eth;cL; & eth; c L ; c R & THORN; . They have the simple but important implication that the amount of energy transmission can never exceed the amount of information transmission. We verify them using the AdS/CFT correspondence, using the perturbation method, and in examples beyond holography. We also show that these inequalities are sharp by constructing a class of interfaces that saturate them.