Universal Bound on Effective Central Charge and Its Saturation

This is the authors' abstract. We don't add key points for this paper.

The effective central charge (denoted by <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>c</a:mi></a:mrow><a:mrow><a:mi>eff</a:mi></a:mrow></a:msub></a:mrow></a:math>) is a measure of entanglement through a conformal interface, while the transmission coefficient (encoded in the coefficient <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>c</c:mi><c:mrow><c:mi>L</c:mi><c:mi>R</c:mi></c:mrow></c:msub></c:math> 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, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mn>0</e:mn><e:mo>≤</e:mo><e:msub><e:mrow><e:mi>c</e:mi></e:mrow><e:mrow><e:mi>L</e:mi><e:mi>R</e:mi></e:mrow></e:msub><e:mo>≤</e:mo><e:msub><e:mrow><e:mi>c</e:mi></e:mrow><e:mrow><e:mi>eff</e:mi></e:mrow></e:msub><e:mo>≤</e:mo><e:mi>min</e:mi><e:mo stretchy="false">(</e:mo><e:msub><e:mrow><e:mi>c</e:mi></e:mrow><e:mrow><e:mi>L</e:mi></e:mrow></e:msub><e:mo>,</e:mo><e:msub><e:mrow><e:mi>c</e:mi></e:mrow><e:mrow><e:mi>R</e:mi></e:mrow></e:msub><e:mo stretchy="false">)</e:mo></e:mrow></e:math>. 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.