Universal Bound on Effective Central Charge and Its Saturation

The effective central charge (denoted by ceff) is a measure of entanglement through a conformal interface, while the transmission coefficient (encoded in the coefficient cLR 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 article, we propose the inequalities, 0 ≤ cLR ≤ ceff ≤ min (cL,cR). 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 and in examples beyond holography. We also show that these inequalities are sharp by constructing a class of interfaces that saturate them.